When someone dies in New York without a will, they are said to have died "intestate," and state intestacy law decides who inherits. The order is specific — the spouse inherits first, then children, then parents, then siblings, and so on through more distant relatives. Nobody in the family gets to decide who receives what; the law makes that determination based on the family relationships at the time of death.
Because there is no will naming an executor, the court appoints an Administrator to manage the estate. This person carries the same responsibilities an executor would — gathering assets, paying debts, and distributing what remains — but they are court-appointed rather than chosen by the deceased. Disagreements among family members are common in intestacy situations and can slow things down considerably, which is one reason families often benefit from a calm, neutral conversation early in the process.