I think it depends on the crime's level of severity. If the child abuser has abused several kids till they died or where mutilated/unable to function as a human being for life, I would sterilize the abuser. But if they've only abused 1-2 children, And they can still function in society, I wouldn't sterilize the abuser.
These people should have any subsequent children they have removed, And random checks to make sure they aren't hiding unregistered children. In addition, They should be put on a very public registry, Much akin to a sex offender, And forbidden to adopt children. These people have the ability to destroy a child's ability to attach to people, Which, A former victim myself, I still have trouble. I practically live in my room because of social anxiety.
People convicted of extreme child abuse should be subject to extreme sterilization, not just sterilization. These people are the dregs of society and deserve absolutely no mercy whatsoever. In fact, it is my sincere belief that these people should be put on death row. These people do not deserve any second chance and society.
I think people convicted of moderate child abuse should be sterilized. Not only will it deter other people from abusing their children, but it's a just punishment. I cannot believe people would actively abuse their own children, such people are a threat to society and they shouldn't be allowed to harm any more children.
There are certain cases of child abuse that are slam dunks as to whether the abuser is qualified to be a parent. In those cases an option for the criminal justice system should be to sterilize them. It seems if you beat one kid to death or lock one in a bathroom for years, then you are not qualified to be a parent.
This type of punishment would be considered cruel and unusual, and as we know, cruel and unusual punishment is against our constitution. Sterilization is an absolutely barbaric thing to do to someone, no matter how heartless or disgusting their crime is. And, if you ask me, it's kinda weird. I just feel its incredibly wrong, and different punishments should be thought, namely in my opinion, keep it the way it is.