Cliffie,
Sometimes the father knows that the child will be surrendered. At that time, I think a father could make a case for custody. Too much of the time, the father is unaware.
Because desperate women left their children to die they were given this alternative in order to save the life of the child. The child becomes a ward of the state and though never having the information about his parents or their support the child has a chance at a life.
C.