While some tend to think that mothers automatically get custody of a child over the father or that a father's visitation rights are based on the decision of the mother, none of this is true under California law. The fact is, both fathers and mothers have equal standing under the law in regard to child custody and visitation law.
California will use the standard of the best interests of the child in determining legal custody and visitation standards. It is possible that a father's rights could be diminished or lost due to abuse or some kind of negative influence, but such allegations would have to be proved, not assumed; otherwise, the father's rights remain intact.
In years gone by, it was almost invariably the mother who received custody of a child, while the father would be allowed visitation rights and have to pay some form of child support. However, it is not nearly as uncommon these days for dads to receive primary custody if it is shown they have a better ability to care for the child and a closer relationship with the child. And fathers with primary custody can seek child support the same way a mother primary custodian can.