how do I begin probate in NY state if my mother died intestate

In California, for an estate under $100,000 in non-real estate assets, there is a summary process to transfer ownership. Also, accounts with transfer on death or pay on death designations would not be included in the estate subject to probate. I'm not sure if this is the case in New York or not. You need to retain a qualified New York probate attorney to answer these questions. Perhaps a NY attorney on AVVO will respond. Good luck.