unmarried mom wants fatherto relinquish rights

What is the name of your state? California

i want the father of my child to relinquish his rights to our newborn daughter. for our safety and for a fresh start. we are not married, but he was at the birth and did sign the paperwork to be on the baby's birth certificate. we were living together but he has repeatedly disappeared since the baby's birth (9 months of age now; he's been gone hald of the time). i'm assuming now that he's run off with the person he recently had an affair with. also, the woman he had been seeing is a violent alcoholic and had threatened to harm the baby and i if he were to stay with us

ABOUT HIM
--french national with a green card and could potentially be a flight risk
--history of substance abuse w/2 strikes still on record

MY QUESTIONS
--what are the steps needed to pursue something like this
--can the court FORCE sole custody to me in case he wouldn't appear
--how can i find out his complete background (i was recently told he may have had a restraining order against him)
--what are my parental rights if he flees the country