If you do not have a will, your estate passes through intestacy. Intestacy just means that you die without a will and that your inheritance is subject to the default rules in New York. Generally, that means your estate would pass to your closest living heirs.
For example if you’re married and have children, the first fifty thousand dollars plus half would pass to your spouse, and the other half to your children.
It’s important to have a will to make sure that your wishes are followed. This is especially important if your closest living relatives are more remote.
If you don’t have a will, your estate needs an administrator. It’s not probate. It’s considered administration, but you still need someone appointed to handle your affairs.
There is a list of priorities according to New York statute as to who gets to be administrator. Spouse has the first priority, followed by children and then down the list of relatives.
Again, it’s important to make sure that you have a will so that you are in control of who’s in charge of your final affairs.