I am six months pregnant and the biological father is not in my life other than when he chooses to be which is very seldom, my question is this, If I don't list him on the birth registration am I able to pursue child support and or full custody. He called it quits two months into this pregnancy and has only talked to me twice in six almost seven months. He has showed no concern for this unborn child and I want to know my rights as far as support or custody.

If you don't list him you make it harder, but not impossible to pursue support. Even if you DO list him and he doesn't sign an acknowledgement of paternity, if you file for a support the court will first order paternity testing to establish him as the legal father. Once the court awards paternity, then he has the full rights AND responsibilities of any parent. You will have to show that you are the best custodian for your child (usually not hard to do). You can then apply for child support.

And if you don't list him, it does not stop him from asking for visits ( and he will get them unless he is a threat to the child)
He is not required to have any relationship with you, as the father of the child he will have rights in court. Listing him or not listing him does not take away those rights, Just as you will have to get a court order for child support and a court order for custody, he has to get a court order for his visits.

If you were thinking that he would not be able to have visits with the child you are mistaken