If paternity has not been established - either by the father acknowledging the fact or via a court ruling, usually obtained when child support is sought - then the unmarried father has no legal custody or visitation rights. So, to be able to exercise your custody rights, you must establish paternity.
In most cases when parents are not married, the father does have a meaningful relationship with his child. However, if he is not living with the mother, he is usually at her mercy when it comes to visitation. If she is remarried or living with another man, this could further complicate the relationship. In fact, the mother could move out of state and take the child with her if an unmarried father has not legally obtained visitation in family court.
There have been cases where the mother has relocated with the child to another state without the birth father's consent. If this happens, usually emergency measures have to be taken, involving a court order to compel the mother to return with the child in a specified period of time.
If you are unmarried and want to have regular access to your child, you should obtain a court-ordered parenting schedule that assures both parents of regularly scheduled visitation time. In addition, the child benefits more from a regular schedule that the parents have worked out between themselves and that has been sanctioned by the court. If this is not done, an unmarried father could remain dependent upon the mother's whims to dictate his relationship with his child.
If paternity has been established and an unmarried father is paying child support, it is still necessary to obtain a court order for visitation. An unmarried father can even seek primary custody of his child if he believes he has a good case and it would be in the child's best interest to remove him or her from the mother's care. The issues that the court must consider in child custody or visitation disputes between unmarried parents are essentially the same as those applied in Arizona divorce cases.
The quantity of parenting time an unmarried father has can also affect the amount of child support he has to pay. And while someone should not request more parenting time in an effort to reduce child support, the amount of parenting time may have a direct bearing on an increase or decrease in support obligations.