What happens to the property/estate when a relative dies and leaves no will. And, this relative has no children and is estranged from his wife.

When someone dies without a will they are said to have died "intestate." The law of the state where they resided at death will dictate how their property passes to their heirs. This law that applies when one dies without a will or trust is commonly referred to as "intestate succession." Whether the estranged wife has lost her status as an heir depends on state law. That state law may provide, for example, that at least a legal separation, if not a divorce decree, would be required for a spouse to lose her status as an heir. Or it may provide that living separately and handling their property separately is all that is required for the spouse to lose her right to inherit from her deceased husband. I do not practice in New York, so I can't be more specific. You should contact a New York attorney who practices estate planning (wills and trusts) and he or she should be able to advise you.