They would both have equal rights to child, legally. Issue becomes what is best for child. That will depend on income, expenses, school, criminal record of parents, who will watch child during day, and many other facts that will be inquired into by judge.
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In Arkansas, we have a statute that specifically states that when a child is born out of wedlock the mother has custody of the child.
The father may petition the Circuit Court for a Decree declaring him to be the father, and when it does so the Court may grant the father visitation rights.
After an adjudication of paternity, the father can then seek custody if he show that he shows that he is a fit parent, has fulfilled his responsibilities as a father, and that it would be in the child's best interest for the father to be awarded custody.
One or both of the parties need to go to court and commence a paternity and custody action to establish paternity, custody and visitation as well as support.
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