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According to NY EPTL 4-1.1 Descent and distribution of a decedent's estate
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.
Thus, under NY law, as long as your mom is alive she is the lawful heir and not the siblings. However, if she has dementia, then this is basis for her children to be named administrators and you can have co-administrators of the estate, but she is the heir.