Strange custody question

I have a 7 year old son and there is no father listed on the birth certificate. Rather, he was listed at the way bottom as a friend. The father was someone who had taken advantage of me while drunk and at the time I was scared to go the road alone and tell people about it so I kept him around. He was at the hospital however he basically was an off the grid child, I later found out, so he had no ID or social security number so he couldn’t be on the birth certificate anyway. He was extremely abusive and I left him after the baby was 2 months old. Literally escaped in the middle of the night. We have no contact. I have since planned on relocating out of country and have supplied them with my sons birth certificate showing I am the only one listed. They need a statute or source of law proving I have the right to take him with me. I have only found the statute about the 4 year rule that paternity is basically too late for him to try and establish. But, I can’t find anything that says single mothers have the right to relocate. It was fine proof for the USA for the passport issuance of him but somehow I need more proof. Any help would be greatly appreciated.