New York Consolidated Laws, Estates, Powers and Trusts Law - EPT § 7-5.3 Payment to beneficiary

(a) If the beneficiary survives the depositor under the circumstances provided in paragraph four of section 7-5.2, the funds shall be paid to the beneficiary upon his order, if, at the time of his demand for payment of all or part of the funds, he is eighteen or more years of age.

(b) If the beneficiary survives the depositor under the circumstances provided in paragraph four of section 7-5.2, and if the beneficiary is under eighteen years of age at the time demand for payment of any part or all of the funds is made, the funds may be paid to the order of the parent or parents of the beneficiary to be held for the use and benefit of such infant beneficiary or to the order of the duly appointed guardian of the property of the beneficiary, if the funds are equal to or are less than ten thousand dollars;  but if the funds are more than ten thousand dollars, the funds may be paid only to the order of the duly appointed guardian of the property of the beneficiary.