Family Law Questions? Ask a Family Lawyer Online.
You should file a petition to terminate his parental rights and have those rights given to you through a court order.
If you cannot find the father to have him served, you can publish a summons in the local newspaper.
My suggestion is that you see a local family law attorney about doing this. If the father has abandoned the child and has no relationship with him, the petition will be well-founded and you should have a great chance to gain custody.