SOLE CUSTODY IN CALIFORNIA (long story)?

so I am a single mother 20. My son is 19 months he last seen his father a year and 4months ago. He was not there for the birth and was in j-hall so he's not on the birth certificate.he lives with his grandma and is not working. I have my own apartment and starting school this fall. He was very violent in the past. When he got out in feb. Of 2010 I attempted to go visit ..for him to see the baby he said he wanted nothing to do with the baby..because I didn't want to be in a relationship with him and tried to micro manage how I spend money on my son. He's never bought any pampers etc. There was a dna test set up and child support but states he has no income.so he doesn't have to pay and hasn't paid since it was established. He said when he finds me at a grocery store he's going to take off with my son and leave to texas. He recently went to my mothers house and made threats. My mother called the cops but they couldn't do anything because he left right before they showed up. I also had all his family members calling my phone saying they will beat my a$$ and take my son. So I had to change my number. I was wondering what to expect out of the process and how will they determine who gets sole custody or joint and how long will the process take. Please detail your answers so I can get a understanding of how all this will play out. THANK YOU