Section 652. Jurisdiction over applications to fix custody in matrimonial actions on referral from supreme court

(a)  When  referred  from  the
  supreme  court to the family court, the family court has jurisdiction to
  determine,  with  the  same  powers  possessed  by  the  supreme  court,
  applications  to  fix temporary or permanent custody and applications to
  modify judgments and orders of custody  or  visitation  in  actions  and
  proceedings  for  marital separation, divorce, annulment of marriage and
  dissolution of marriage. Applications to modify judgments and orders  of
  custody  may be granted by the family court under this section only upon
  the showing to the family court that there has been a subsequent  change
  of circumstances and that modification is required.
    (b) In the event no such referral has been made and unless the supreme
  court  provides  in the order or judgment awarding custody or visitation
  in an action for divorce,  separation  or  annulment,  that  it  may  be
  enforced  or  modified  only in the supreme court, the family court may:
  (i) determine an application to enforce the order or  judgment  awarding
  custody  or  visitation,  or (ii) determine an application to modify the
  order or judgment awarding custody or visitation  upon  a  showing  that
  there  has been a subsequent change of circumstances and modification is
  required.
    (c) In any determination of an application pursuant to  this  section,
  the family court shall have jurisdiction to determine such applications,
  in  accordance  with subdivision one of section two hundred forty of the
  domestic relations law, with the same powers possessed  by  the  supreme
  court,  and the family court's disposition of any such application is an
  order of the family court appealable only under article eleven  of  this
  act.