If I had sole physical custody of my child because the father is unfitt and something happened to me would the father get her.

My childs father has an extensive domestic violence background and he's been to prison for it a couple of times, he doesn't see or call his child nor does he pay child support. I have found out it's rather hard to get a father's rights terminated so to make sure my child wouldn't go to her father if something happened to me should I get sole physical custody of my child? If I was granted sole physical custody does that mean that her father couldn't ever get custody if something happened to me. What are my options on what I should do? - Is this your question? Add additional information