You can not unless he is unfit.
In most places, a 16-year-old cannot legally move out without parental consent. If a minor leaves home without permission, the parents or legal guardians can involve the authorities. It is important to discuss your situation with a trusted adult or seek guidance from a social worker to explore options within the legal framework.
Emancipation is a matter for the courts and for the person (people) who do have legal custody of you. As your cousin does not have custody, you cousin has nothing to say about whether you can be emancipated.
It is your cousin also
They would be a cousin once removed.
A minor can not move anywhere without parental consent.
your 5th cousin
He is your cousin
cousin
your 2nd cousin, or maybe your 2nd cousin once removed.
Your cousin.
Your first cousin
cousin