In New York, the answer is that most of your assets will go through probate. This includes real estate, personal property, and financial accounts. If the deceased person had a valid will, their assets will be distributed according to the terms of the will. If they did not have a will, their assets will be distributed according to state law.
In either case, the Surrogate's Court must approve the distribution of assets before they can be transferred to the rightful heirs. The probate process can be complex, so it is important to seek legal assistance if you are named as an executor in a will or if you are an heir to an estate.