Section 81. Appointment of guardians by parent

A married woman is a joint
  guardian of her children with her husband, with equal powers, rights and
  duties in regard to them. Upon the death of either father or mother, the
  surviving parent, whether of full age or a minor, of a child  likely  to
  be  born,  or  of  any  living child under the age of eighteen years and
  unmarried, may, by deed or last will,  duly  executed,  dispose  of  the
  custody  and  tuition  of such child during its minority or for any less
  time, to any person or persons. Such  surviving  parent  may  appoint  a
  guardian  or  guardians  of the person and of the property of the infant
  and in making such appointment shall not be limited to  the  appointment
  of  the  same person or persons in both capacities. Either the father or
  mother may in the life-time of them both, by last  will  duly  executed,
  appoint the other the guardian of the person and property of such child,
  during  its minority.   Either the father or mother may in the life-time
  of them both by last will duly executed, and with the written consent of
  the other duly acknowledged, appoint the other and a third person to  be
  the  guardians  of  the  person  and  property  of such child during its
  minority, and in making such appointment shall not  be  limited  to  the
  appointment  of  the  same  person  or  persons in both capacities. Such
  consent must have as part thereof a sworn statement that the  consenting
  parent in so consenting, is motivated solely by the welfare of the child
  or  children,  the  guardianship of whom is the subject of such consent,
  and that such consenting parent has not received and  will  not  receive
  any  consideration  for such consent, and such consent may be revoked by
  such consenting parent at any time prior to the death of the  other,  by
  filing  in  the  office  of the county clerk of the county in which said
  other then resides, a written revocation of such consent, subscribed and
  acknowledged by the person so revoking, with proof of service of a  copy
  thereof  on  such  other  parent in the manner provided for service of a
  summons. An appointment of a guardian of the person and property  of  an
  infant  made by duly executed last will of his father or mother shall be
  valid and effective if at the time the will is admitted to  probate  the
  other  parent  shall have died or the surviving parent be an adjudicated
  incompetent. If both parents die under  circumstances  which  render  it
  difficult  or  impossible to determine which of them died first and both
  of them left last wills appointing the  same  person  as  guardian,  the
  appointment  shall  be  valid  and  effective. If both parents die under
  circumstances which render it difficult or impossible to determine which
  of them died first, leaving last wills appointing different  persons  as
  guardians,   the   surrogate's   court  shall  determine  which  of  the
  appointments will best serve the welfare of the child and issue  letters
  of  guardianship  accordingly. If at any time during the minority of the
  infant the surviving parent becomes competent to serve as  guardian,  he
  may  apply  to  the  court  which  issued letters of guardianship to the
  guardian appointed by will for a decree revoking such  letters  and  the
  court  shall  on  such  application make such order or decree as justice
  requires.   A person appointed guardian in  pursuance  of  this  section
  shall  not  exercise  the power of authority thereof unless such will is
  admitted to probate, or such deed executed and recorded as  provided  by
  SCPA 1710.