I lived on my own since I was 15 years old.
Your biggest problem is you are only thirteen. It's almost impossible to find a job that will allow you to earn enough money at that age to live alone. If you somehow have a large amount of money already (high unlikely but hey) then a child must get "divorced" emancipated (sp i think thats the word) from his parents. This is literally impossible unless there is a good reason.
So no, you cannot really do anything legally until you are 18.