do unmarried fathers have any rights?

Under California law, fathers, whether married or not, have equal custodial rights, absent a court order to the contrary.  Legal and physical custody of each parent is determined either by agremeent or by the court, and is based on the best interests of the child.  To assert and preserve your custodial rights and visitation rights, and the rights of your child to a relationship with you, you must file a Parentage Action, also known as a paternity action.  You may also file a Request for Order, seeking specific custodial rights and visitation time.  Of course, you may also be responsible for child support, under the California Statewide Guidelines, as will the child's mother. The amount of support payable by either parent is generally based on adjusted gross income and the amount of custodial time each parent has.