I am pregnant and the babies father is going after custody or visitation when the child is born. He is very abusive and does have a violent record from the past. He is been making many threats towards me and my unborn child. He has even stated that once he has the child in his hands he stated that he would mess the child up in the head to get back at me for leaving him and that he may even run away with the child. This is definitely someone that should never be left alone with a child. Unfortunately, I wish I was able to see that sooner. I also am wondering if it is possible or how difficult it would be for him to get any custody or visitation if his name is not put on the birth certificate.

You need to get an order of protection.Save any of his messages and when the baby is born ,you can show this to the court.Get the order of protection NOW. For your own safety.
DNA determines paternity,who is on the birth certificate is of little consequence.

"He" can do nothing until the child is born. If he wants visitation with the child he then has to go to Court and apply for custody or visitation. You respond by asking for support. The Court will require DNA - to prove paternity - and will review the circumstances and PROOF and then determine what is best for the child.

If he is the father he has rights but he cannot exercise those rights without a Court Order.

I'm sure this varies a lot from state to state but in California, where I am, you can get orders on custody (you or he) before the child is born that will apply upon the birth of the child. This is useful because we all know there can be some lag time between the time a child is born and the time the court can make these orders. And if you've got an emergency, like a wacky dad, you may need some sort of protection now (or at least it might make you feel better).

If there have been treats of abduction, or DV on the dad's part, get a restraining order. If you are in California get a pre-birth custody order giving you sole physical and legal custody (you can get this as part of a restraining order in our state).

If you are outside of California check with local counsel and see if you can get some custody orders that will apply upon the birth of the child or the best way to handle it.

What you need to do is document the threats, the abusive behavior and everything else. If you have to carry an electronic memo recorder with you.

If you can prove what you say, then he is unlikley to get custody and you may be able to stop visitation.

He is definitely unlikely to get primary custody until the child is older, unless he can prove you are totally unfit.

But don't leave his name off the because that's only a delaying tactic.

First many men make threats so you will not sue for child support, or to try and control you.

First not what you "know" but what can you prove in court, what evidence that an attorney will be able to sure in court. Police reports where he hurt you or someone perhaps,

To play the other side, you are saying you don't want him to have the child, so just like he is saying he will take the child and not let you see them, you are basically saying the same thing for your reasons.

But visists are fought out in court, even being a threat, he will get supervised visits at least