WALKER, Circuit Judge:
Defendants Cesar A. Perales, Commissioner of the New York State Department of Social Services (“State defendant” or “State commissioner”), Francis T. Purcell, Executive of the County of Nassau, and Joseph A. D’Elia, Commissioner of the Nassau County Department of Social Services (“County defendants”), appeal from a judgment entered in the United States District Court for the Eastern District of New York (Glasser, J.) awarding the plaintiff class attorney’s fees to be satisfied jointly and severally by the defendants in their official capacities pursuant to 42 U.S.C. § 1988. Because we agree with the district court that both the State and County defendants may be held liable for attorney’s fees and because we find that the district court’s imposition of joint and several liability was within its discretion, we affirm.
BACKGROUND
This appeal arises out of a class action brought in 1982 by the plaintiffs pursuant to 42 U.S.C. § 1983 on behalf of homeless families in Nassau County. Plaintiffs alleged that the defendants had failed to provide adequate emergency shelter to homeless families eligible for such shelter in violation of, inter alia, the Social Security Act, 42 U.S.C. §§ 601, et seq., and various provisions of the New York Social Services Law. Specifically, the complaint alleged that the County defendants, acting under color of state law, denied plaintiffs emergency shelter and, in some cases, written notice of its decision not to provide such shelter in violation of the Social Security Act and the equal protection and due process clauses of the United States Constitution. Koster v. Webb, 598 F.Supp. 1134, 1136 (E.D.N.Y.1983). Plaintiffs charged the State defendant with “failure to insure that the state policy and practice of providing emergency shelter to homeless families is in effect in Nassau County.” The amended complaint sought damages and declaratory and injunctive relief requiring the defendants to provide “lawful emergency shelter to meet the plaintiffs’ needs and to consider each and every request for emergency shelter and provide written notice of any denials thereof.”
The district court denied the County defendants’ motion to dismiss the complaint for failure to state a claim upon which relief could be granted, holding that the plaintiffs had stated a claim under 42 U.S.C. § 1983 for a right to emergency shelter under the Social Security Act, as well as pendent state law claims for similar relief under the New York Constitution and Social Services Law. Id. After considerable discovery, the State commissioner moved for summary judgment. While that motion was pending and after lengthy negotiations, the parties entered a stipulation [134] of settlement approved by the district court on March 18, 1987.
The settlement agreement, which explicitly left the issue of attorney’s fees unresolved, provides that “the County must act in response to an eligible family's request for emergency housing on the same day that the request is made; must ensure that the emergency housing provided meets certain minimum standards; must give prompt written notice of any decision of ineligibility; and must provide these services on a 24-hour day [sic] basis, seven days a week.” Koster v. Perales, No. 82 Civ. 2892, slip op. at 2, 1989 WL 79482 (E.D. N.Y. July 11, 1989). In addition, it provides that the State commissioner shall supervise the County to assure that it complies with the agreement.
Upon application, the district court concluded that the plaintiffs were prevailing parties within the meaning of 42 U.S.C. § 1988 and, as such, were entitled to attorney’s fees. The court awarded plaintiffs $326,678.07 in fees against the defendants, jointly and severally. This appeal followed.
DISCUSSION
A. Plaintiffs’ Eligibility for Counsel Fees
The State commissioner challenges the district court’s conclusion that the plaintiffs prevailed against him, a condition precedent to any award of attorney’s fees pursuant to 42 U.S.C. § 1988. First, the State commissioner contends that the relief the plaintiffs obtained in the settlement bears no relationship to the claims raised or the relief sought in the complaint. Next, he argues that the plaintiffs are not prevailing parties because the settlement provides no benefits to plaintiffs other than those that the State is already obligated to provide under existing law. Finally, he maintains that his obligation to supervise the County’s implementation of the State’s emergency shelter policy does not raise a federal claim sufficient to support the jurisdiction of the federal court.
Title 42 U.S.C. § 1988 provides, in pertinent part, that the court in its discretion may allow a “prevailing party” in a section 1983 action to recover reasonable attorney’s fees. “ ‘[P]laintiffs may be considered “prevailing parties” for attorney’s fees purposes if they succeed on any significant issue in litigation which achieves some of the benefit the parties sought in bringing the suit.’ ” Texas State Teachers Ass’n v. Garland Indep. School Dist., — U.S.-, 109 S.Ct. 1486,1491, 103 L.Ed.2d 866 (1989) (quoting Nadeau v. Helgemoe, 581 F.2d 275, 278-79 (1st Cir.1978)). At a minimum, the plaintiff must demonstrate a change in the legal relationship between itself and the defendant arising from the resolution of the lawsuit. Id. 109 S.Ct. at 1493. However, relief need not be judicially decreed in order to justify a fee award under § 1988.
A lawsuit sometimes produces voluntary action by the defendant that affords the plaintiff all or some of the relief he sought through a judgment — e.g., a monetary settlement or a change in conduct that redresses the plaintiffs’ grievances. When that occurs, the plaintiff is deemed to have prevailed despite the absence of a formal judgment in his favor.
Hewitt v. Helms, 482 U.S. 755, 760-61, 107 S.Ct. 2672, 2675-76, 96 L.Ed.2d 654 (1987) (citing Maher v. Gagne, 448 U.S. 122, 129, 100 S.Ct. 2570, 2575, 65 L.Ed.2d 653 (1980)); see also McCann v. Coughlin, 698 F.2d 112, 128 (2d Cir.1983).
In applying the prevailing party standard, it is helpful to identify the relief sought by the plaintiff and compare it with the relief obtained as a result of the suit. See Institutionalized Juveniles v. Sec’y of Pub. Welfare, 758 F.2d 897, 911 (3d Cir.1985) (citing Bonnes v. Long, 599 F.2d 1316, 1319 (4th Cir.1979), cert. denied, 455 U.S. 961, 102 S.Ct. 1476, 71 L.Ed.2d 681 (1982) (look to the complaint to identify the conditions the suit sought to change, then use this as a benchmark to measure relief ultimately obtained)). A plaintiff may be considered a prevailing party even though the relief ultimately obtained is not identical to the relief demanded in the complaint, provided the relief obtained is of the same [135] general type. See Institutionalized Juveniles, 758 F.2d at 912.
Applying these principles to the facts before us, we agree with the district court that the plaintiffs have prevailed against the State commissioner within the meaning of section 1988 and thus are eligible for a fee award. The amended complaint explicitly charges Commissioner Pe-rales with “failure to insure that the state policy and practice of providing emergency shelter to homeless families is in effect in Nassau County” in violation of the Social Security Act, the Code of Federal Regulations, 42 U.S.C. § 1983 and the New York Social Services Law. Under the terms of the settlement agreement, the commissioner agreed to remedy these violations by undertaking to “supervise the Nassau County defendants in accordance with applicable federal and state laws and regulations to assure that the County defendants comply with the provisions of this stipulation that are in accordance with such applicable laws and regulations ...” Plaintiffs therefore obtained the relief contemplated at the outset of the litigation. In fact, the plaintiffs obtained the full scope of relief they sought against the State commissioner.
Commissioner Perales argues that this relief is an insufficient basis for an award of attorney’s fees because under the terms of the settlement agreement he agreed to do no more than what he is already required to do by law—supervise the County to insure that the State’s emergency shelter policy is in effect. We agree with the district court that despite the fact that the shelter policy was in place before the litigation and the State commissioner had a preexisting duty to supervise its implementation, “that policy lay dormant and virtually ignored by the State and County defendants.” Koster v. Perales, slip op. at 9. As the district court noted, as a result of this litigation and the settlement agreement, the State has “shifted [its] position toward the plaintiff classmembers from one of inaction and noncompliance to one of action and compliance.” Id.
Next, the State defendant challenges the role of this lawsuit in changing state policy to ensure that Nassau County provides adequate emergency shelter to homeless families. He maintains that the plaintiffs have failed to prove any causal nexus between the documented improvement in both the availability and conditions of emergency shelter and the State’s renewed promise in the settlement agreement to supervise the County’s compliance with state policy.
To justify a fee award, “the prevailing party must show a causal connection between the relief obtained and the litigation in which the fees are sought.” Gerena-Valentin v. Koch, 739 F.2d 755, 758 (2d Cir.1984). Such a causal connection exists if the plaintiff’s lawsuit was “a catalytic, necessary, or substantial factor in attaining the relief.” Id. at 758-59 (quoting Commissioners Court of Medina County v. United States, 683 F.2d 435, 440 (D.C.Cir.1982). Because this inquiry is primarily a factual matter, the district court’s findings with respect to causation will not be disturbed unless they are clearly erroneous. Id. at 759.
The district court’s finding that the County’s improved compliance with the State shelter policy was due, at least in part, to the State commissioner’s stipulated supervision, is not clearly erroneous. Prior to the settlement, emergency shelter services in Nassau were substandard, indicating a failure of State supervision because, presumably, the State commissioner would have ordered compliance if he had been aware of the problems identified in the complaint. Plaintiffs submitted affidavits and news articles documenting both the decline in reports of homeless families in substandard housing in the County since the settlement agreement was entered into and the County’s adherence to the terms of the settlement agreement. These submissions were a sufficient basis for the district court’s inference that the improvements resulted from the stipulation since it is logical to assume that the improvements are a product of both the County’s compliance with State policy and the State’s supervision of the County to ensure compliance. [136] Under these circumstances, it is neither necessary nor possible to dissect the improvements to isolate their immediate cause.
Finally, the State commissioner contends that the plaintiffs’ claim that the State failed to supervise the County pursuant to 42 U.S.C. § 602(a)(3) does not state a violation of federal law upon which federal court jurisdiction may be predicated consistent with the eleventh amendment. He argues that such jurisdiction depends upon “a specific conflict between a state plan or practice on the one hand and a federal mandate on the other.” Oberlander v. Perales, 740 F.2d 116, 119 (2d Cir.1984).
We agree with the district court which twice rejected the State commissioner’s contention that his failure to supervise did not violate federal law. See Koster v. Webb, 598 F.Supp. 1134, 1137 (E.D.N.Y.1893); Koster v. Perales, 108 F.R.D. 46, 53-54 (E.D.N.Y.1985). The Social Security Act requires a state to supervise any plan which the state establishes under the Aid to Families with Dependent Children program (AFDC). Section 602(a)(3) of the Act provides:
A State plan for aid and services to needy families with children must ... (3) either provide for the establishment or designation of a single State agency to administer the plan, or provide for the establishment or designation of a single State agency to supervise the administration of the plan.
This provision has been interpreted to require states not only to establish an entity to supervise the administration of their AFDC plans, but also to carry out that supervision. See Almenares v. Wyman, 334 F.Supp. 512, 517 (S.D.N.Y.), aff'd, 453 F.2d 1075 (2d Cir.1971), cert. denied, 405 U.S. 944, 92 S.Ct. 962, 30 L.Ed.2d 815 (1972). The cases relied upon by the State are inapposite as they do not involve violations of the Social Security Act or any other federal statute. See, e.g., Rush v. Smith, 573 F.2d 110, 115 (2d Cir.1978) (challenged procedure did not violate any specific provision of the Social Security Act); Oberlander v. Perales, 740 F.2d at 119 (violation of state regulation). Here, by contrast, plaintiffs charged the State commissioner with violating the provisions of the Act.
The district court need not have determined whether plaintiffs would have prevailed on the merits in order to find that the complaint presented a substantial federal claim supporting federal jurisdiction and upon which an award of attorney’s fees could be predicated. Rather, the court need only have determined that the plaintiffs’ claims were not “frivolous, unreasonable or groundless.” Christiansburg Garment Co. v. E.E.O.C., 434 U.S. 412, 422, 98 S.Ct. 694, 701, 54 L.Ed.2d 648 (1978). The federal claims in this action clearly pass this test. Accordingly, we agree with the district court that the plaintiffs prevailed against the State commissioner within the meaning of § 1988, and, therefore, are entitled to attorney’s fees.
B. Allocation of Fee Liability
1. County Liability
The County defendants do not contest the plaintiffs’ status as prevailing parties in this litigation. Rather, they contend that if the plaintiffs are entitled to attorney’s fees, the award must be satisfied in full by the State. We agree with the district court that the County defendants may be held liable for the satisfaction of the fee award.
The County defendants maintain that they are not liable for attorney’s fees because under New York Social Services Law § 65(3) 1, county commissioners of social services are merely agents of the New York Department of Social Services which has ultimate policy making authority. Local social services commissioners, they contend, merely effectuate the policies of the State commissioner, and therefore, under [137] the reasoning of Unger v. Blum, 117 A.D.2d 607, 498 N.Y.S.2d 154 (2d Dep’t 1986), and Beaudoin v. Toia, 45 N.Y.2d 343, 408 N.Y.S.2d 417, 380 N.E.2d 246 (1978), they should not be held responsible for fees. We are not persuaded by this argument.
As an initial matter, it appears that the agency defense, to the extent it applies here, would be available only to defendant Joseph D’Elia, Commissioner of the Nassau County Department of Social Services as the New York Social Services Law designates the county commissioners of public welfare agents of the State Department of Social Services. The County Executive is not implicated by the statute. Moreover, assuming without deciding the accuracy of the County commissioner’s reading of Un-ger and Beaudoin, we nonetheless conclude that these New York cases do not shield him from liability for attorney’s fees either.
Because a request for attorney’s fees under § 1988 is made pursuant to a federal statute, the court must look to federal rather than state law to determine ultimate fee liability, Shadis v. Beal, 685 F.2d 824, 828 (3d Cir.), cert. denied, 459 U.S. 970, 103 S.Ct. 300, 74 L.Ed.2d 282 (1982), though state law frequently determines the nature of obligations on which such liability depends. As a matter of federal law, an agent is liable for the torts he commits, “ ‘whether or not he has been authorized or even directed to commit [them].’ ” Pennhurst State School & Hospital v. Halderman, 465 U.S. 89, 113 n. 23, 104 S.Ct. 900, 915 n. 23, 79 L.Ed.2d 67 (1984) (quoting Larson v. Domestic & Foreign Commerce Corp., 337 U.S. 682, 694, 69 S.Ct. 1457, 1463, 93 L.Ed. 1628 (1949); Farid v. Smith, 850 F.2d 917, 921 (2d Cir.1988). Accordingly, courts have held that where, as here, the County is responsible for the administration of the State’s social services program, see generally, New York Social Services Law §§ 22(9)(d), 34, 65(3), a fee award against the County is not inappropriate despite the State’s supervisory role. See Holly v. Lavine, 605 F.2d 638, 643-45 (2d Cir.1979), cert. denied, 446 U.S. 913, 100 S.Ct. 1843, 64 L.Ed.2d 266 (1980) (fees awarded against County as well as State commissioner of social services for denial of AFDC benefits to an illegal alien based on state Social Services Law); Mendoza v. Blum, 602 F.Supp. 200, 204 (S.D.N. Y.), aff'd without opinion, 767 F.2d 908 (2d Cir.1985).
The cases cited by the County do not alter the outcome of this case. Unger stands for the proposition that the State commissioner remains solely liable for attorney’s fees where a claim is brought challenging the validity of a state fair hearing decision affirming a local social service agency’s initial determination. The Unger court reasoned that because the County commissioner is bound by the decisions of the State Department of Social Services made after a statutory fair hearing and simply effectuates the determinations of the State, it is the State commissioner who should be held liable for attorney’s fees. Unger, 498 N.Y.S.2d at 155. In the context of fair hearings, the County commissioner has no independent legal responsibility and no discretion; he simply executes the will of the State commissioner. Applying similar reasoning in Beaudoin, the New York Court of Appeals held that a County commissioner lacks standing to challenge a state fair hearing decision because, in interpreting State Department of Social Services regulations, the County commissioner may not substitute his judgment for that of the State. Instead, he must comply with the State’s policy which is contained in each fair hearing decision.
Neither Unger nor Beaudoin insulates the County from responsibility for attorney’s fees here. Unlike the situation in Unger where the County’s only role was that of agent of the State effectuating a State fair hearing decision, here the district court found that the County commissioner has an independent statutory duty, distinct from his obligation as an agent of the State, to “administer the public assistance and care ... of persons in need in the territory over which he has jurisdiction.” New York Social Services Law § 65(1). The complaint challenged not just the State’s but also the County’s own policy [138] and practice of denying emergency shelter to homeless families, and the County agreed in the stipulation of settlement to insure that its policies and practices afford the plaintiffs adequate emergency shelter. Thus, the County’s contention that this case concerns only State policy for which the County as agent of the State may not be held liable, is untenable and its reliance on Unger misplaced.
Moreover, in Unger, although the petitioner actually sued the local agency for discontinuing her AFDC grant, she was in essence challenging the State’s decision affirming the local agency’s determination. Significantly, the County in that case merely implemented what the court later concluded was an invalid State'decision. The court therefore held that the State was solely responsible for the payment of the petitioner’s attorney’s fees. Here, by contrast, the plaintiffs challenged the County’s failure to implement the State’s valid, preexisting emergency shelter policy, the implementation of which was primarily the County’s responsibility. See, e.g., Toia v. Regan, 54 A.D.2d 46, 387 N.Y.S.2d 309, 312 (4th Dep’t), aff'd, 40 N.Y.2d 837, 387 N.Y. S.2d 832, 356 N.E.2d 276 (1976), appeal dismissed, 429 U.S. 1082, 97 S.Ct. 1087, 51 L.Ed.2d 528 (1977). The plaintiffs sought to compel the County defendants to comply with the shelter policy and the terms of the settlement agreement to which the County itself is a signatory ensure such compliance.2 Under these circumstances, Unger does not preclude an award of attorney’s fees against the County.
It is the basic philosophy of § 1988 that fee liability runs with merits liability in the underlying action. Kentucky v. Graham, 473 U.S. 159, 170-71, 105 S.Ct. 3099, 3107-08, 87 L.Ed.2d 114 (1985). While it is true that this action was settled without a judicial determination of the merits, such a determination is not a necessary predicate to a fee award. “ ‘[PJarties may be considered to have prevailed when they vindicate rights through a consent judgment or without formally obtaining relief.’ ” Maher v. Gagne, 448 U.S. 122, 129, 100 S.Ct. 2570, 2575, 65 L.Ed.2d 653 (1979) (citation omitted). The County defendants do not challenge the district court’s determination that the plaintiffs prevailed against them. Indeed, these defendants agreed to provide substantial relief to the plaintiffs in the stipulation of settlement. Accordingly, the award of fees against the County is consistent with the philosophy of § 1988.
2. Joint and Several Liability
The State defendant contends that if the plaintiffs have prevailed against him, he is responsible for no more than ten percent of the fee award. We are not persuaded. Given the State’s significant role in the events prompting this lawsuit, the district court was within its discretion in holding the State and County defendants jointly and severally responsible for the fee award.
Focusing on the relative degree of culpability among the State and County defendants, the district court concluded that given the “interrelationship and overlap between their responsibilities and obligations with respect to the emergency shelter program at issue here, both under law and under the settlement agreement, an attempt to precisely balance the amount of responsibility rightfully placed upon either side would seem both a futile and wasteful task for [it] to undertake.” Koster v. Perales, slip op. at 21. The State maintains [139] that this conclusion was ah abuse of the court’s discretion for several reasons. First, it argues that the district court had a duty to apportion attorney’s fees. Next, it asserts that joint and several liability is permissible in only four narrowly defined circumstances, none of which is present here. Finally, the State contends that the court erred in failing to consider the time plaintiffs spent litigating against each defendant. We are not persuaded by these contentions.
The allocation of fee liability is a matter committed to the district court’s discretion and will not be disturbed unless the determination evidences an abuse of discretion. See Hensley v. Eckerhart, 461 U.S. 424, 437, 103 S.Ct. 1933, 1941, 76 L.Ed.2d 40 (1982). Although the law governing apportionment of attorney’s fees assessments remains relatively unsettled, see Grendel’s Den Inc. v. Larkin, 749 F.2d 945, 959 (1st Cir.1984), district courts have appropriately considered a variety of factors in allocating fee liability including the relative culpability of the parties, see Jose P. v. Ambach, 669 F.2d 865, 871 (2d Cir.1982), and the proportion of time spent litigating against each defendant, see Tongol v. Donovan, 762 F.2d 727, 729 (9th Cir.1985); see also Vulcan Soc. of Westchester Cty. v. Fire Dept., 533 F.Supp. 1054, 1064 (S.D.N.Y.1982).
On the basis of these considerations, the district court may allocate the fee award between the responsible parties, setting the percentage for which each is liable where the claims against the defendants are separate and distinct or where culpability is significantly unequal, Crosby v. Bowling, 683 F.2d 1068, 1075 (7th Cir.1982), or it may hold the responsible parties jointly and severally liable for the fee award. The only limitation on the district court’s discretion to award fees jointly and severally is that it must do so consistently with the pre-existing background of substantive liability rules. See Kentucky v. Graham, 473 U.S. at 171, 105 S.Ct. at 3108; Dean v. Gladney, 621 F.2d 1331, 1339-40 (5th Cir.1980), cert. denied, 450 U.S. 983, 101 S.Ct. 1521, 67 L.Ed.2d 819 (1981) (defendants must be joint tortfeasors). Of course, the district court should “make every effort to achieve the most fair and sensible solution that is possible.” Grendel’s Den, 749 F.2d at 960.
Thus, although apportionment may in some cases be a more equitable resolution, there is no rule in this circuit that requires it whenever possible. Here Judge Glasser determined that apportionment was neither necessary nor possible given the interrelationship among the defendants and their overlapping responsibilities with respect to the shelter program. He acknowledged that although the terms of the settlement agreement designate the County as the entity with primary responsibility for the provision of shelter services, the agreement also emphasizes the State’s supervisory responsibilities. Although the State attempts to downplay the importance of its supervisory role, we believe that, as the facts of this case show, the State’s role cannot be trivialized. Had the State carried out its duty to supervise County implementation of the shelter policy from the outset, it might well have remedied the problem, obviating the need for this litigation altogether.
Moreover, we agree with the district court that despite the exclusively supervisory responsibility that the settlement agreement imposes on the State, federal and state law contemplate an active comprehensive State role. Federal regulations provide that the State retain authority and discretion in the areas of policy and rule-making, conduct periodic evaluations, ensure continuous program operation and disseminate information to staff. See 45 C.F.R. §§ 205.100 and 205.120. Similarly, the New York Social Services Law directs the State to set guidelines and standards. See New York Social Services Law §§ 20, 22, 34. Accordingly, the responsibility of the two defendants in this case is not significantly unequal as to make joint and several liability unjust. Spell v. McDaniel, 616 F.Supp. 1069, 1115 (E.D.N.C.1985), aff'd in part, vacated in part on other grounds, 824 F.2d 1380 (4th Cir.1987), cert. [140] denied, 484 U.S. 1027, 108 S.Ct. 752, 98 L.Ed.2d 765 (1988).3
The State’s argument that joint and several liability for attorney’s fees is not appropriate except in specific limited situations need not be addressed since, as the State acknowledges, joint and several liability is appropriate where the action or in action of several defendants produces a single indivisible injury. Dean v. Gladney, 621 F.2d at 1339. Here, the district court found that both the State and County defendants ignored the emergency homeless shelter policy. The result was an indivisible injury — simply stated, plaintiffs did not receive adequate emergency shelter. Accordingly, the district court did not abuse its discretion in imposing joint and several liability for the fee award.
Finally, the State claims that the district court’s failure to apportion attorney’s fees on the basis of the time the plaintiffs spent litigating against each defendant was an abuse of discretion. Specifically, the State maintains that it should not be charged for the 76.75 hours the plaintiffs spent in opposing the County’s motion to dismiss or the time spent on discovery against the County defendants. Plaintiffs point out that the 76 hours represent only 3% of the 2,296 hours they devoted to this litigation. Furthermore, the record indicates that the plaintiffs spent three times as many hours opposing the State’s summary judgment motion and that much of the balance of the plaintiffs’ time was devoted to activities involving both defendants. Under these circumstances, and in view of our desire to avoid transforming the “consideration of a fee petition [into a] ‘second major litigation,’ ” Webb v. Dyer County Bd. of Ed., 471 U.S. 234, 244 n. 20, 105 S.Ct. 1923,1929 n. 20, 85 L.Ed.2d 233 (1985) (quoting Hensley v. Eckerhart, 461 U.S. at 442, 103 S.Ct. at 1944 (Brennan, J., concurring in part and dissenting in part)), we hold that the district court’s imposition of joint and several fee liability was a proper exercise of its discretion. Accordingly, the judgment of the district court is affirmed in all respects.