Duffly, J.
We are asked to decide whether child custody provisions of a divorce judgment of the Probate and Family Court may be challenged by the plaintiff, E.N. (father), in a subsequent proceeding. The father claims that the Probate and Family Court lacked jurisdiction over the issue of custody as it [183]*183relates to the parties’ older child, who was bom in Puerto Rico. Without the father’s consent, the defendant, E.S. (mother), removed that child to Massachusetts where she has family, there obtaining an abuse prevention order on allegations of abuse by the father that were, in a later proceeding, credited by a judge of the Probate and Family Court following trial.
The father did not appeal the October 22, 2001, judgment of divorce nisi awarding to the mother sole legal and physical custody of that child and of a second child who was bom to the parties in Massachusetts, following their separation.1 Instead, well over a year later, on December 17, 2002, the father filed a complaint for modification in the Probate and Family Court alleging a change in the children’s circumstances and requesting sole legal and physical custody and the right to remove the children to Puerto Rico, as well as modification of his support obligations. On the day scheduled for trial on the modification complaint (and other consolidated matters, see infra), the father filed a motion pursuant to G. L. c. 209B, § 12(a), seeking recognition and enforcement in the Probate and Family Court of a judgment of the Superior Court of Bayamón, Puerto Rico, dated April 18, 2001, granting him custody of the older child. The father also filed a “motion to dismiss,” in essence challenging the authority of the court to exercise jurisdiction with respect to the older child. After a trial, the probate judge rejected the father’s jurisdictional arguments. Treating the motion as an alternative claim for relief, the judge then proceeded to address the merits of the father’s complaint and denied the father’s request to modify the divorce judgment and remove the children to Puerto Rico.
Our resolution of the issues differs somewhat from that of the probate judge, whose decision we affirm. We conclude that, under applicable provisions of the Massachusetts Child Custody Jurisdiction Act (MCCJA), G. L. c. 209B, and the Parental Kidnapping Prevention Act (PKPA), 28 U.S.C. § 1738A (1994 & Supp. 2006), Massachusetts had jurisdiction to issue an initial custody determination; such jurisdiction was properly exercised in connection with the mother’s divorce action.
[184]*184Background, facts and proceedings. The parties were married in Puerto Rico on April 15, 1996, and the first of the two children was bom there on March 26, 1997. The marriage was unhappy and, as found by the probate judge, beginning in 1999, the father was “physically, verbally, and emotionally abusive to the [mother] and the children.”* 2 The parties separated on October 15, 1999; on October 18, the father filed a custody petition in Puerto Rico, alleging that the mother had abandoned the child.3 Following a hearing in Puerto Rico (not attended by the mother), the father was awarded temporary custody of the child until January 31, 2000, when the order expired.4 After a brief reconciliation that ended in January, 2000, the mother became pregnant with the parties’ younger son. See note 2, [185]*185supra. They separated again, and on March 1, 2000, the mother relocated to Massachusetts without the older child, initially renting a room in her sister’s house.
In July, 2000, then some six months pregnant, the mother returned to Puerto Rico. On July 25, 2000, she asked that the father allow her to spend some time with the older child. Rather than return the child to the father at the end of the day, as she apparently had promised, the mother removed the child to Massachusetts.
The next day, July 26, 2000, the mother — citing a two-year history of physical and emotional abuse by the father against her and the child — obtained in the Probate and Family Court an abuse prevention order against the father that also awarded her custody of the older child.* 5
Meanwhile, in Puerto Rico, the father sought to initiate criminal proceedings against the mother. On August 28, 2000, a judge of “the Court of First Instance, Bayamón Part,” issued a warrant for the mother’s arrest on the ground of an asserted violation of the Puerto Rico Penal Code.6 On January 18, 2001, the mother was arrested on the warrant and detained at the Barnstable house of correction.
Upon the mother’s arrest, the older child was briefly placed in the custody of the Department of Social Services (department).7 That same day, the father traveled to Massachusetts to retrieve the older child and was interviewed by the department concerning the allegations of abuse the mother had made against him in connection with the restraining order of July 26, 2000. The next day, January 19, 2001, the maternal grandmother filed in the Probate and Family Court a petition for temporary guardianship, in which she asserted the need to [186]*186protect the children from abuse by the father. The father filed an opposition to the petition. A hearing was held, and on January 19, 2001, a judge of the Probate and Family Court8 granted temporary custody of both children to the maternal grandmother, to expire on April 19, 2001.
In his findings on the order for temporary guardianship, the probate judge found that Puerto Rico was then the home State9 of the older child and that Massachusetts was the home State of the younger child.10,11 The probate judge entered his order pursuant to the emergency jurisdiction provision of the MCCJA, G. L. c. 209B, § 2(a)(3), on findings that an emergency existed and that the older child may have been subject to mistreatment and neglect by either or both parents.12
On February 12, 2001, the father filed a petition for habeas corpus in the Superior Court of Bayamón, Puerto Rico, request[187]*187ing that the court grant him custody of and “patria potestas” over the older child.13 The older child had not lived in Puerto Rico for the six-month period preceding the filing of this petition, and thus Puerto Rico was not then the child’s home State.
On April 13, 2001 — by which time the older child had lived in Massachusetts for nearly nine consecutive months — the mother filed a complaint for divorce in the Probate and Family Court, requesting, among other things, custody of the children. The father, who concedes he was served with process, filed an answer to the complaint stating that the Probate and Family Court lacked jurisdiction over the custody of the older child. Referring to the facts that the child was bom in Puerto Rico and that “the cases [regarding custody of the child] started in the court of Puerto Rico and in the jurisdiction of Puerto Rico [in] October 18, 1999,” the father claimed in his answer that “[p]ursuant to the provisions of sec. 1738A of the Parental Kidnapping Prevention Act of 1980, Puerto Rico is the state with jurisdiction over the [older child].”
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Duffly, J.
We are asked to decide whether child custody provisions of a divorce judgment of the Probate and Family Court may be challenged by the plaintiff, E.N. (father), in a subsequent proceeding. The father claims that the Probate and Family Court lacked jurisdiction over the issue of custody as it [183]*183relates to the parties’ older child, who was bom in Puerto Rico. Without the father’s consent, the defendant, E.S. (mother), removed that child to Massachusetts where she has family, there obtaining an abuse prevention order on allegations of abuse by the father that were, in a later proceeding, credited by a judge of the Probate and Family Court following trial.
The father did not appeal the October 22, 2001, judgment of divorce nisi awarding to the mother sole legal and physical custody of that child and of a second child who was bom to the parties in Massachusetts, following their separation.1 Instead, well over a year later, on December 17, 2002, the father filed a complaint for modification in the Probate and Family Court alleging a change in the children’s circumstances and requesting sole legal and physical custody and the right to remove the children to Puerto Rico, as well as modification of his support obligations. On the day scheduled for trial on the modification complaint (and other consolidated matters, see infra), the father filed a motion pursuant to G. L. c. 209B, § 12(a), seeking recognition and enforcement in the Probate and Family Court of a judgment of the Superior Court of Bayamón, Puerto Rico, dated April 18, 2001, granting him custody of the older child. The father also filed a “motion to dismiss,” in essence challenging the authority of the court to exercise jurisdiction with respect to the older child. After a trial, the probate judge rejected the father’s jurisdictional arguments. Treating the motion as an alternative claim for relief, the judge then proceeded to address the merits of the father’s complaint and denied the father’s request to modify the divorce judgment and remove the children to Puerto Rico.
Our resolution of the issues differs somewhat from that of the probate judge, whose decision we affirm. We conclude that, under applicable provisions of the Massachusetts Child Custody Jurisdiction Act (MCCJA), G. L. c. 209B, and the Parental Kidnapping Prevention Act (PKPA), 28 U.S.C. § 1738A (1994 & Supp. 2006), Massachusetts had jurisdiction to issue an initial custody determination; such jurisdiction was properly exercised in connection with the mother’s divorce action.
[184]*184Background, facts and proceedings. The parties were married in Puerto Rico on April 15, 1996, and the first of the two children was bom there on March 26, 1997. The marriage was unhappy and, as found by the probate judge, beginning in 1999, the father was “physically, verbally, and emotionally abusive to the [mother] and the children.”* 2 The parties separated on October 15, 1999; on October 18, the father filed a custody petition in Puerto Rico, alleging that the mother had abandoned the child.3 Following a hearing in Puerto Rico (not attended by the mother), the father was awarded temporary custody of the child until January 31, 2000, when the order expired.4 After a brief reconciliation that ended in January, 2000, the mother became pregnant with the parties’ younger son. See note 2, [185]*185supra. They separated again, and on March 1, 2000, the mother relocated to Massachusetts without the older child, initially renting a room in her sister’s house.
In July, 2000, then some six months pregnant, the mother returned to Puerto Rico. On July 25, 2000, she asked that the father allow her to spend some time with the older child. Rather than return the child to the father at the end of the day, as she apparently had promised, the mother removed the child to Massachusetts.
The next day, July 26, 2000, the mother — citing a two-year history of physical and emotional abuse by the father against her and the child — obtained in the Probate and Family Court an abuse prevention order against the father that also awarded her custody of the older child.* 5
Meanwhile, in Puerto Rico, the father sought to initiate criminal proceedings against the mother. On August 28, 2000, a judge of “the Court of First Instance, Bayamón Part,” issued a warrant for the mother’s arrest on the ground of an asserted violation of the Puerto Rico Penal Code.6 On January 18, 2001, the mother was arrested on the warrant and detained at the Barnstable house of correction.
Upon the mother’s arrest, the older child was briefly placed in the custody of the Department of Social Services (department).7 That same day, the father traveled to Massachusetts to retrieve the older child and was interviewed by the department concerning the allegations of abuse the mother had made against him in connection with the restraining order of July 26, 2000. The next day, January 19, 2001, the maternal grandmother filed in the Probate and Family Court a petition for temporary guardianship, in which she asserted the need to [186]*186protect the children from abuse by the father. The father filed an opposition to the petition. A hearing was held, and on January 19, 2001, a judge of the Probate and Family Court8 granted temporary custody of both children to the maternal grandmother, to expire on April 19, 2001.
In his findings on the order for temporary guardianship, the probate judge found that Puerto Rico was then the home State9 of the older child and that Massachusetts was the home State of the younger child.10,11 The probate judge entered his order pursuant to the emergency jurisdiction provision of the MCCJA, G. L. c. 209B, § 2(a)(3), on findings that an emergency existed and that the older child may have been subject to mistreatment and neglect by either or both parents.12
On February 12, 2001, the father filed a petition for habeas corpus in the Superior Court of Bayamón, Puerto Rico, request[187]*187ing that the court grant him custody of and “patria potestas” over the older child.13 The older child had not lived in Puerto Rico for the six-month period preceding the filing of this petition, and thus Puerto Rico was not then the child’s home State.
On April 13, 2001 — by which time the older child had lived in Massachusetts for nearly nine consecutive months — the mother filed a complaint for divorce in the Probate and Family Court, requesting, among other things, custody of the children. The father, who concedes he was served with process, filed an answer to the complaint stating that the Probate and Family Court lacked jurisdiction over the custody of the older child. Referring to the facts that the child was bom in Puerto Rico and that “the cases [regarding custody of the child] started in the court of Puerto Rico and in the jurisdiction of Puerto Rico [in] October 18, 1999,” the father claimed in his answer that “[p]ursuant to the provisions of sec. 1738A of the Parental Kidnapping Prevention Act of 1980, Puerto Rico is the state with jurisdiction over the [older child].”
A judgment of the Superior Court of Bayamón dated April 18, 2001 (and bearing a certificate of authentication dated April 19, 2001),14 granted the father’s petition for custody and patria [188]*188potestas over the older child and ordered that the child be brought immediately to the jurisdiction of Puerto Rico.15
In the meantime, the mother’s divorce action proceeded in Massachusetts; temporary orders issued June 20, 2001, awarding her sole legal and physical custody of the children and directing the father to pay $100 per week for support of the mother and the children. In a memorandum and order on the motion for temporary orders issued the same day, the probate judge determined that Massachusetts had “subject matter” jurisdiction over the older child’s custody on the basis that “no custody order had been in effect from another jurisdiction on either July 26, 2000 [when the abuse prevention order first issued], or [on] August 23, 2000 [when the restraining order was renewed],” and also “pursuant to G. L. c. 209B, § 2(a)(3)” (conferring emergency jurisdiction if the child is physically present in the Commonwealth and “it is necessary in an emergency to protect the child from abuse or neglect”).16
[189]*189On October 22, 2001, after a hearing before the probate judge (not attended by the father), a judgment of divorce nisi issued that, among other things, awarded the mother sole legal and physical custody of the children, ordered the father to pay $100 per week as child support (plus an additional $25 per week towards established arrearages), and divided the parties’ property. The father (who concedes that he received a copy of the divorce judgment) did not appeal from the divorce judgment.
Also in October, 2001, a judgment entered dismissing the maternal grandmother’s guardianship petition. A year later, on November 22, 2002, the maternal grandmother filed a second petition for temporary guardianship of the parties’ children. In this petition, she alleged that the children had been neglected by the mother and also had been physically and possibly sexually abused by the mother’s live-in boyfriend. The probate judge issued an order for temporary guardianship that same day.
Thereafter, on December 16, 2002, the father filed the within complaint seeking modification of the divorce judgment. In the complaint, the father acknowledged that the mother had earlier been awarded sole legal and physical custody of the children; he alleged as changed circumstances that, among other things, the children had been placed with the maternal grandmother as a result of an ongoing investigation in Massachusetts of abuse and neglect. The father requested that the divorce judgment be modified by granting him sole legal and physical custody of the children and the right to remove them to Puerto Rico. The mother responded with a complaint for contempt against the father alleging that he had failed to pay support as ordered.
On June 26, 2003, the day scheduled for trial of the pending consolidated actions — the father’s complaint for modification, the mother’s complaint for contempt, and the maternal grandmother’s petition for guardianship — the father, through counsel, filed a “motion to domesticate foreign decree under G. L. c. 209B, § 12(a),” requesting that the Puerto Rico habeas corpus judgment granting him custody of the older child be [190]*190given full faith and credit. He also filed a motion to dismiss the modification and guardianship proceedings, alleging that the Probate and Family Court lacked jurisdiction under the MC-CJA, G.L. c. 209B, § 2(d), and the PKPA, 28 U.S.C. § 1738A(a). According to the father, because the Puerto Rico Superior Court’s resolution of the custody issue (see note 15, supra) predated that of the probate judge’s June 20, 2001, determination that Massachusetts had jurisdiction, the guardianship and modification actions should be dismissed and the Puer-to Rico court’s April 18, 2001, judgment enforced.17
Following trial on the consolidated actions, the probate judge denied the father’s request for modification of the divorce custody order, dismissed the petition for guardianship, and adjudged the father in contempt for wilfully neglecting and refusing to pay child support. The judge concluded that the Probate and Family Court was not precluded from exercising jurisdiction with respect to the older child18 and, on the merits of the complaint for modification and removal, that the father [191]*191had failed to demonstrate that a change in custody and the removal of the children to Puerto Rico would be in their best interests. The father appealed.
Discussion. 1. Claimed lack of jurisdiction. The father argues, among other things, that, because Puerto Rico was the older child’s home State and had “reasserted” its “jurisdiction over the matter”19 after emergency jurisdiction in Massachusetts was no longer necessary, the Puerto Rico habeas corpus judgment is entitled to full faith and credit and the probate judge erred in maintaining jurisdiction over the older child. The father asks that the Puerto Rico judgment “be ordered registered in [Massachusetts], thus ordering compliance with its rulings, and ordering the return of [the older child] to Puerto Rico with the father.” The father’s arguments are premised on the assumption that the Probate and Family Court lacked “subject matter” jurisdiction and therefore was not competent to adjudicate the custody matter in the context of the parties’ divorce action.
We think the question is not whether, strictly speaking, the Probate and Family Court had “subject matter” jurisdiction — [192]*192in the sense of having been vested by the Legislature with the power to decide the custody issue, see Doe v. Roe, 377 Mass. 616, 617 (1979)20 — but rather whether, under applicable provisions of the PKPA and MCCJA, the Probate and Family Court should have exercised jurisdiction to issue the divorce judgment awarding custody.21 This requires a two-stage inquiry: first, whether Massachusetts was the home State when the mother’s divorce action was filed, thus giving the Probate and Family Court “authority to exercise jurisdiction” under the MCCJA, Khan v. Saminni, 446 Mass. 88, 91 (2006); second, whether the court should have exercised such jurisdiction under provisions of the MCCJA and PKPA. See, e.g., id. at 95-96 (Trinidad court was vested with authority to adjudicate a custody issue under its laws; that Massachusetts was the home State “is not determinative of jurisdiction”). See also Custody of Brandon, 407 Mass. 1, 5 (1990); Bak v. Bak, 24 Mass. App. Ct. 608, 614-615 (1987).
Under the MCCJA, “[a]ny [Massachusetts] court which is competent to decide child custody matters has jurisdiction to [193]*193make a custody determination” if Massachusetts was the home State of the child on the commencement of the divorce action.22 G. L. c. 209B, § 2(a)(l)(i). The probate courts are competent to decide custody matters, as they have been vested by the Legislature with “exclusive original jurisdiction ... of actions relative to the care, custody, education and maintenance of minor children.” G. L. c. 215, § 4, as amended by St. 1975, c. 400, § 54. “Home state” is defined as “the state in which the child immediately preceding the date of commencement of the custody proceeding resided with ... a parent ... for at least 6 consecutive months.” G. L. c. 209B, § 1. See 28 U.S.C. § 1738A(b)(4), (c)(2)(A). See also Custody of Brandon, 407 Mass. at 7, 14 (“Section 2[a][1] of G. L. c. 209B grants jurisdiction based solely on residence in the Commonwealth for at least six months of the child and a parent or person acting as a parent. . . . Section 1738A[c][2] of the [PKPA] grants ‘home state’ jurisdiction under the same six-month requirement found in G. L. c. 209B”). Here, the mother and the older child had been living in Massachusetts for nearly nine consecutive months (and the mother had been a Massachusetts resident for over thirteen months) when she commenced the divorce action on April 13, 2001; thus, the Probate and Family Court had home State jurisdiction to make the custody determination in connection with the divorce.
Notwithstanding that the Probate and Family Court had jurisdiction to decide the custody issue, we must next consider whether the exercise of jurisdiction was appropriate. To satisfy the requirements of both the MCCJA and the PKPA, the custody proceeding must not have commenced “during the pendency of a proceeding in a court of another state” exercising jurisdiction consistently with applicable provisions of the MCCJA and PKPA. See G. L. c. 209B, § (2)(d); 28 U.S.C. § 1738A(g).23
[194]*194Prior to commencement of the divorce action on April 13, 2001, only the father’s habeas corpus petition, filed February 12, 2001, was pending. To be subject to enforcement in Massachusetts, that petition, which gave rise to the Puerto Rico court’s custody determination, must have been filed at a time when Puerto Rico had home State jurisdiction — that is, Puerto Rico must have been the home State of the child “within six months before the date of the commencement of the [habeas corpus] proceeding.” 28 U.S.C. § 1738A(c)(2)(A)(ii). See note 23, supra. Because the child left Puerto Rico with the mother on July 25, 2000 — at a time when there was no outstanding order awarding custody and patria potestas to the father or prohibiting the child’s removal24 — Puerto Rico was no longer the child’s home State and had not been within the six months [195]*195preceding the February 12, 2001, filing of the habeas corpus action.
Even if Puerto Rico was no longer the child’s home State, however, the judgment on the habeas corpus petition could still be subject to enforcement (and the Probate and Family Court precluded from “modifying” that judgment) if Puerto Rico had “continuing jurisdiction” under the PKPA at the time the judgment was made. That is, if Puerto Rico had made a prior child custody determination consistently with provisions of the PKPA, jurisdiction “continues as long as the requirement of subsection (c)(1) of this section continues to be met and such State remains the residence of the child or of any contestant.” 28 U.S.C. § 1738A(d). See note 23, supra; Hillier v. Hillier, 41 Mass. App. Ct. 486, 488-489 (1996) (although Massachusetts was the home State pursuant to G. L. c. 209B, § 2, the Probate and Family Court was precluded from exercising jurisdiction under the PKPA, where a Florida court had continuing jurisdiction).
The father makes no proper appellate argument that the court in Puerto Rico was entitled to invoke the continuing jurisdiction provision of the PKPA when it issued the habeas corpus judg[196]*196ment on April 18, 2001.25 See Cameron v. Carelli, 39 Mass. [197]*197App. Ct. 81, 85 (1995). Although he alluded to the issue in his motion to dismiss, he abandoned the issue on appeal. In light of the father’s abandonment of any argument concerning continuing jurisdiction, and the views of the Bayamón Superior Court judge as to the basis for that court’s jurisdiction, see note 25, supra, we consider the issue no further.
When the mother filed the divorce action on April 13, 2001, the older child had been living with her in Massachusetts for nearly nine months, and the child was not the subject of a previously issued valid judgment or order of the Puerto Rico courts awarding custody to the father. When the father filed his habeas corpus petition on February 12, 2001, the older child had not resided in Puerto Rico for the six months preceding the filing. Whether couched in terms of subject matter jurisdiction or home State jurisdiction as defined by the PKPA and MCCJA, we conclude that Massachusetts had jurisdiction over the custody issue and that it was properly exercised.26
2. Modification. Contrary to the father’s contention, the [198]*198probate judge did not abuse his discretion by declining to modify the divorce judgment to award the father sole legal and physical custody of the children or to allow the father to remove the children to Puerto Rico. See G. L. c. 208, § 28, as amended by St. 1993, c. 460, § 60 (“Upon a complaint after a divorce . . . the court may make a judgment modifying its earlier judgment as to the care and custody of the minor children of the parties provided that the court finds that a material and substantial change in the circumstances of the parties has occurred and the judgment of modification is necessary in the best interests of the children”); G. L. c. 208, § 30 (the Massachusetts “removal statute”). See also Rosenthal v. Maney, 51 Mass. App. Ct. 257, 266 (2001) (best interests of the child always remain the paramount concern in a removal case). Although the evidence reflects that the mother had experienced significant parenting problems in the past and the children were removed from her custody for periods of time arising in part because they had allegedly been abused by her former boyfriend (against whom there is an abuse prevention order on behalf of the children), the judge found that the children now live with the mother in her own apartment, that the mother (who works) receives assistance from her mother in caring for the children, that the mother’s home is clean and organized, and that the children are “well-dressed and clean and doing well in school and day care respectively.” In addition, the judge found that the mother is no longer in an abusive relationship with her former boyfriend, she “has engaged in counseling to explore preventing future relationships involving domestic violence,” and has been “successful at not re-engaging in relationships involving domestic violence.”
The judge also made findings concerning the physical and emotional abuse inflicted by the father on the mother and the older child during the marriage. See note 2, supra. The judge concluded that the father had failed to show that “the quality of the children’s lives would at all be improved by a move to Puer-[199]*199to Rico, emotionally, physically, or developmentally,” or that the removal of the children to Puerto Rico was in the best interests of the children. To the contrary, the judge found that “[i]n light of the parties’ violent history, removal of the children from the Commonwealth is not in either child’s best interest.” There was no error.
Modification judgment dated October 23, 2003, affirmed.