N.Y. SCP. LAW § 1409 : NY Code - Section 1409: Notice of probate 1

Before  letters  are  issued  there  shall be filed in the court a
  notice entitled in the proceeding stating the name of the testator,  the
  name and address of the proponent, and that the will of the testator has
  been  offered  for  probate  or probated, as the case may be. The notice
  shall further set forth the name and post-office address of each  person
  named  or referred to in the petition who has not been served or has not
  appeared or waived service of  process  and  shall  state  whether  such
  person is named or referred to in the will as legatee, devisee, trustee,
  guardian  or  substitute or successor executor, trustee or guardian. The
  notice shall further set forth the name and post-office address  of  the
  attorney  general  of  the  state  of New York if the will that has been
  offered for probate contains a charitable bequest which is either to  an
  unnamed   charitable  organization  or  is  in  an  unspecified  amount,
  including but not limited to, a bequest of all or part of the  residuary
  estate.
    (a)  Where  by  the  terms of the will an interest in a trust or other
  fund or property has been limited in any contingency to the persons  who
  shall  compose  a  certain class upon the happening of a future event it
  shall be sufficient to name only the persons in being at  the  death  of
  the  decedent  who would constitute the class if such event had happened
  immediately before the date of such notice, and who have not been served
  or appeared or waived service of process.
    (b) Where by the terms of the will an interest in  a  trust  or  other
  fund  or  property  has  been  limited  to a person who is named in such
  notice or who has been served  or  has  appeared  or  waived  notice  of
  process,  and  has  been  further limited upon the happening of a future
  event to a class of persons described in terms of their relationship  to
  such person it shall not be necessary to name such class of persons.
    2.  There  shall  be  filed  with the notice proof by affidavit of the
  mailing of a copy thereof  to  each  of  the  persons  required  by  the
  preceding  subdivision  to be named in such notice, and if any person is
  an infant or an incompetent, of the mailing of a  copy  thereof  to  the
  person  or  persons upon whom personal service of process is required to
  be made with respect to the infant or incompetent. When  it  appears  by
  the petition for probate that the name or address of any person referred
  to  in  this  section  is  unknown  mailing to such person of the notice
  herein described shall not be required.
    3. Upon the probate of an estate and distribution of  its  assets,  if
  any, under this chapter, if an undistributed asset is subsequently found
  by  the estate, the surrogate's court that granted such probate petition
  shall maintain jurisdiction and shall not require any additional service
  of the notice required by this section to be served again by the estate,
  unless such previously undiscovered asset has an estimated value of more
  than five thousand dollars or it has been more than  seven  years  since
  the distribution of the assets pursuant to the original probate.