If you break up, your partner generally will have custody and visitation rights only if the partner is also a parent of the child. Then, he or she will have the same rights to child custody or visitation a married person would have. Such rights are based on the parent-child relationship – not on whether the parents are married. But the law in this area is still developing, and many states allow judges to grant visitation rights to non-parents. Your partner may, of course gain rights or obligations by adopting your child. One may become a legal parent by adoption as well as by natural processes. Adoption is probably the only way that same-sex couples can share custody of a child.