When a person dies without leaving a Last Will and Testament, it's said that they died intestate. When a person dies intestate, that person's property is distributed according to the law. In New York, that law is found in EPTL 4-1.1 (Estates, Powers and Trusts Law).
Who gets what depends on who the living relatives are and their relationship to the Decedent, the person who died. The family members who are entitled to a share of the Decedent's estate when there is no will are called “distributees.”
If the Decedent has…
-A spouse (husband or wife) and no children, then the spouse inherits everything.
-Children* but no spouse, then the children inherit everything.
-Spouse and children*, then the spouse inherits the first $50,000 plus half of the balance. The children* inherit everything else.
-Parents but no spouse and no children*, then the parents inherit everything.
-Siblings (brothers or sisters) but no spouse, children*, or parents, then the siblings inherit everything.
*If a child dies before the Decedent and had children of their own, then the Decedent would have grandchildren. Those grandchildren would step into the Decedent's child's place and inherit in place of the child.