If the custodian of the account dies, a new custodian would take over the account. A successor can be designated at any time by naming the successor in the custodian's will or by signing a letter of designation before a witness. If the deceased custodian had not specified their successor, the new custodian would be named in accordance with applicable state laws listed on the account. If, on the other hand, a child who the account was established for dies before their state's mandated transfer age, the custodial account is considered part of the child's estate and is distributed according to the state's laws.