Custody with absent father.

It depends on the child's age and on the father. If it has been a long time since your child was born and the father has never been interested in seeing the child, I would not worry about filing paperwork to seek custody of your child. Right now, you have 100% custody. If you don't file any papers, it will most likely continue in the same manner for many years, maybe forever. However, if you file paperwork, he might object and then the court would give him some percentage of custody.

The later he files for custody, the better for you. The courts in CA are usually reluctant to change the child's circumstances too much. So, if the child has been only with you for many years, it would be very unlikely that the father would get a lot of custody even if he wanted to.

However, you should not be thinking only about yourself in considering this question. It is presumed that it is in the child's best interest to have “frequent and continuing contact with both parents." Even though you might not think so now, it probably still would be very beneficial for your child to have at least some contact with the father (unless the circumstances clearly state otherwise.) So, towards this goal, you might want to encourage the contact with the father.

Also, unless the father is unemployed, I think you should go for child support. Your child has the right to be cared for by both parents, not by you alone, and you should not deprive your child of this right. Don't forget, of course, that if you apply for a child support, custody question will come up inevitably (which is not necessarily a bad thing, as I described above.)