I'm going to be a single mother soon, and I would like to know how do I go about getting the father to relinquish custody? I know that as the mother, I have full custody unless the father contest and tries to receive visitation, but to avoid that in the future, I would like him to just relinquish custody now. I also know that I can't force him too, but I believe he may be willing to give up custody. What steps should I take to get that done?

Since giving up custody has nothing to do with child support, there is no good reason for him to give up any rights. You can ask him, and if he agrees have an attorney do the paper work, but he will have to understand that he could be forced to pay child support anyway.

And actually no, you may have phsycial custody right now, but you don't have full custody, since the father has equal custody rights to the chlld until a court rules on it, So for your protection you need to get legal custody of the child in addition to child support order