Next of kin hierarchy under NYS law goes as follows:

Surviving spouse

Children

Grandchildren

Parents

Siblings and issue of pre-deceased siblings, if any (nieces and nephews)

Grandparents and issue of predeceased grandparents (first cousins)

Great-grandparents and issue of predeceased great-grandparents (first cousins once removed).

If there isn't a will, things get interesting under NYS law:

quote The property of a decedent not disposed of by will shall be distributed as provided in this section. In computing said distribution, debts, administration expenses and reasonable funeral expenses shall be deducted but all estate taxes shall be disregarded, except that nothing contained herein relieves a distributee from contributing to all such taxes the amounts apportioned against him or her under 2-1.8. Distribution shall then be as follows:

(a) If a decedent is survived by:

(1) A spouse and issue, fifty thousand dollars and one-half of the residue to the spouse, and the balance thereof to the issue by representation.

(2) A spouse and no issue, the whole to the spouse.

(3) Issue and no spouse, the whole to the issue, by representation.

(4) One or both parents, and no spouse and no issue, the whole to the surviving parent or parents.

(5) Issue of parents, and no spouse, issue or parent, the whole to the issue of the parents, by representation.

(6) One or more grandparents or the issue of grandparents (as hereinafter defined), and no spouse, issue, parent or issue of parents, onehalf to the surviving grandparent or grandparents of one parental side, or if neither of them survives the decedent, to their issue, by representation, and the other one-half to the surviving grandparent or grandparents of the other parental side, or if neither of them survives the decedent, to their issue, by representation; provided that if the decedent was not survived by a grandparent or grandparents on one side or by the issue of such grandparents, the whole to the surviving grandparent or grandparents on the other side, or if neither of them survives the decedent, to their issue, by representation, in the same manner as the one-half. For the purposes of this subparagraph, issue of grandparents shall not include issue more remote than grandchildren of such grandparents.

(7) Great-grandchildren of grandparents, and no spouse, issue, parent, issue of parents, grandparent, children of grandparents or grandchildren of grandparents, one-half to the great-grandchildren of the grandparents of one parental side, per capita, and the other one-half to the great-grandchildren of the grandparents of the other parental side, per capita; provided that if the decedent was not survived by great-grandchildren of grandparents on one side, the whole to the great-grandchildren of grandparents on the other side, in the same manner as the one-half.

(b) For all purposes of this section, decedent’s relatives of the half blood shall be treated as if they were relatives of the whole blood.

(c) Distributees of the decedent, conceived before his or her death but born alive thereafter, take as if they were born in his or her lifetime.

(d) The right of an adopted child to take a distributive share and the right of succession to the estate of an adopted child continue as provided in the domestic relations law.

(e) A distributive share passing to a surviving spouse under this section is in lieu of any right of dower to which such spouse may be entitled.

Under NYS law following are not subject to probate: Tenancy by the Entireties (Joint ownership for spouses applies to real estate, bank accounts) ) , Transfer on Death (Bank Accounts), Beneficiary (Life insurance, Annuity), Pay on Death (Bank Accounts), Joint title with right of survivorship (bank accounts, real estate), Homestead Property (primary residence of Florida domicile).

Everything else goes through probate.