1. When a custodianship has been established for a minor, the court may authorize the custodian to accept and receive into the custodianship any additional property that belongs to the minor, with or without bond and with or without court supervision, upon such terms and conditions as the court may require.
2. If the court determines under chapter 475 that full administration of a minor's estate is not required, the court may designate and direct that all or a part of the property owned by the minor be transferred to any adult person or financial institution, including a court-appointed conservator or guardian, to hold and administer under sections 404.005 to 404.094 as custodian for the minor, with or without bond and with or without court supervision, upon such terms and conditions as the court may require.
3. A custodian has no right, because of designation as custodian to possession, control, income or proceeds of any property belonging to the minor that is not transferred to the custodian by the minor, a donor or a person indebted to the minor, except as authorized by the court under subsection * 2 of this section.