An affidavit of heirship is sometimes called an affidavit of kinship. There is no official form, but Queens Surrogate's Court has provided a sample as have many books in the public access law libraries.
Surrogate's Court Rule 207.16 (c) requires that "[w] henever there is a sole distributee (including solely a wife or just one child), an Affidavit of Heirship is required to demonstrate to the court that someone other than the distributee is confirming that there is no other legal heir.
"The regulation also requires an Affidavit of Heirship whenever the distributees are other than a spouse, children or parents. Thus, whenever grandparents, aunts/uncles, cousins, nieces/nephews or more remote relatives are the only distributees, an Affidavit of Heirship must be provided."
§ 7:82. Parties who must be served—Distributees determined under EPTL—Affidavit of Heirship required to identify sole or remote distributees, 1 Harris N.Y. Estates: Probate Admin. & Litigation § 7:82 (6th ed.)