For the loss of parental rights, add the concept of involuntary and imposed by the court.
Or it could be in reference to producing a child for a legal reason, such as surrendering a child to the non-custodial parent for visitation or surrendering a child to the juvenile judicial system. I would contact your local family court and ask someone there about a specific definition.
The phrase "possibilities to surrender" is used to ask someone if he or she is willing to give in to the accusations. This term is commonly used when the accused has no other alternatives to defend him or her.