There are fewer words that cause me so much revulsion as the term "Baby's Daddy". What it leaves you with is a clear picture of a child who has been bastardized because some idiot didn't know how to use a condom. It paints a picture of someone who fails to support their child. This duty of support is so fundamental in the State of Arkansas that it exists even without court order.
All child support can go back to the day of the birth of the child. In fact that is the most common occurrence. The father can be held liable for laying in costs and the costs incurred during the birth. A father who has not established Paternity is called a putative father and has no rights at all. He gains rights when his parentage is recognized by the Court System and he both 1. Maintains a relationship with his child and 2. helps to support his child according to his means. Oftentimes you will be supporting the child by providing food, shelter, medical treatment and clothing. It would behoove you to retain checks, receipts, and to cultivate witnesses outside your family if possible that can testify to your actions which benefit your child.
The first thing to do as a "Baby's Daddy" is to get on the birth certificate by signing an affidavit of paternity. This can be set aside through the use of a DNA test to show that "Baby's Daddy" is someone else. Secondly you will want to establish your rights in a court of law, and, depending on the situation, you will probably want a DNA test performed. Really. Even if you trust her. So what do you do now that you have legal rights?
Usually, as a legally recognized father, you begin with visitation. At some point you can move for custody if it is in the child's best interest if you have followed my advice so far. By the way, this advice is applicable to Arkansas only.
Going for custody is more expensive and your involvement with the child's life to that point has to be significant. You lose a lot when you have a child out of wedlock and you are the guy. You have to fight for your rights immediately. Ideally, the mother of your child should support your efforts so there is no legal fight at all. Most often though, there is a fight just out of spite in a majority of the cases where the father is establishing his status to the child(ren) and demanding his visitation/custody.
Visitation is not only easier, it is a good fall back position if your going for custody. Really a no brainer. Especially since if you haven't provided support and developed a meaningful relationship (i.e. the child knows your his/her father) with the child visitation is about all your going to get. You should check your jurisdiction for standardized visitation guidelines.
Drug use, criminal convictions of certain types, and where you live are just some of the factors that can determine your visitation. Even if you and your lover are going to agree, you need to run everything by an attorney.