If a person dies without leaving a will, a relative, such as a spouse, child, brother or sister, can apply to the Surrogate's Court to be appointed administrator of the estate of the deceased person.
If the estate is valued at $20,000 or less, a simplified procedure is available. It is called "voluntary administration" and normally all that needs to be done is to prepare a form affidavit and file it in the Surrogate's Court. The Court will issue certificates that can be used to collect the assets of the estate and pay any bills incurred by the deceased person.
If the estate is greater than $20,000 in value, a petition asking for the appointment of an administrator of the estate must be filed in Surrogate's Court. Once the Court approves the petition, letters of administration will be issued by the clerk of the Court, usually to the person signing the petition. That person will then take possession of the estate's assets and property, pay any bills, taxes and administration expenses that may be incurred and then distribute whatever is left to the relatives of the deceased specified in the law of intestacy (in New York, the Estates, Powers and Trusts Law Section 4-1.1.)
The process is not called probate because probate signifies that a will is in existence.
-- Richard A. Whitney