N.J. Stat. § 46:38-32
Upon the death of a custodian or renunciation of a custodian designee for whom a successor custodian has been designated or provided by law, the certificate of death, a written renunciation or a written recital of the renunciation, as the case may be, shall be full warrant to all persons for immediate transfer of the custodial property to the successor if the minor is then under 21 years of age. The successor shall cause each security which is custodial property and in registered form to be registered, and each account with a broker or in a bank to be carried, in the name of the successor custodian, or a trust company, followed by substantially the following language: "as custodian for ........................ (name of minor) under the New Jersey Uniform Gifts to Minors Act"; and shall cause each such security and all other custodial property to be delivered to him together with any additional instruments required for the transfer thereof.
N.J.S. § 46:38-32