Subject to subsections (b) and (c) of this section, a person not subject to § 13-305 or § 13-306 of this subtitle who holds property of or owes a liquidated debt to a minor not having a conservator may make an irrevocable transfer to a custodian for the benefit of the minor pursuant to § 13-309 of this subtitle. If a person having the right to do so under § 13-303 of this subtitle has nominated a custodian under that section to receive the custodial property, the transfer must be made to that person. If no custodian has been nominated under § 13-303 of this subtitle, or all persons so nominated as custodian die before the transfer or are unable, decline, or are ineligible to serve, a transfer under this section may be made to an adult member of the minor’s family or to a trust company unless the property exceeds $10,000 in value.