(a) The court is vested with jurisdiction to appoint a guardian of the person or property of any child and with jurisdiction over proceedings involving any child whose custody is the subject of controversy. Any such appointment shall be made pursuant to the same requirements of notice and hearing as are provided for appointments of guardians of the persons and properties of minors by the judge of the probate court.

(b) Courts of record, in handling divorce, alimony, or habeas corpus cases involving the custody of a child or children, may transfer the question of the determination of custody and support to the juvenile court for investigation and a report back to the superior court or for investigation and determination. If the referral is for investigation and determination, then the juvenile court shall proceed to handle the matter in the same manner as though the action originated under this article in compliance with the order of the superior court. At any time prior to the determination of such question, the juvenile court may transfer the jurisdiction of the question back to the referring superior court.