Final answer:
In New York, when a person dies intestate, the surviving spouse receives the first $50,000 plus half of the balance of the estate, and the children inherit the rest. The ex-wife is not entitled to any part of the estate.
Step-by-step explanation:
According to New York intestacy laws, when a person like Lyle dies without a will, known as dying intestate, the distribution of his estate is dictated by state law. If Lyle has a spouse and children, the spouse would typically be the first in line to inherit. Specifically in New York, the surviving spouse would receive the first $50,000 of the estate plus half of the balance, and the remaining estate would then be divided equally among the children. Lyle's ex-wife would not be entitled to any portion of the estate as her rights typically end with the divorce unless specified otherwise in divorce decrees or settlement agreements.