What are the circumstances where a judge would grant emancipation?

This differ between states but in general you have to be 16 to apply and you have to have a income and a place to live. You can not be relying on someone else but take of yourself like an adult. There are more requirements but it differs as I said. If you also are close to the legal age in your state and is abused they can allow it even if you don't fill all the requirements.