I was just thinking about this the other day. My father died when I was six. Normally, he would have been allowed to sell me into slavery until I turned 12. So from 6-12, who had that power? Did anyone have that power?
I’m almost sure no one can sell a daughter except the father (Ein Adam Morish Zechus’e B’ito Le’bno), but the Mother & Brothers have the right to marry a girl under 12 off. She has the right at the age 12 to “undo” the marriage.
For your information, “mide-oraisa’ (biblically speaking) only the father can give his daughter away in marriage (and sell her – but that is aslo a way to marriage-see mishpotim).The chachomim allowed a mother and brothers to marry her of but she has the right- at maturity- to reject these kiddushim. it is called “mi-un”. gavra-at-work is fulyl correct in his posting.
There is no “custody”, the children fend for themselves. BD or the father can appoint someone over the estate (as ICOT points out), but the children are “free” to collect (as per the Mishna in BB 139b) if they have no Yerusha.