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If the parents are married see links below
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Wait until you're 18.
If a 14 year old wants to live with the dad and the mother has custody, she can live in Nevada with the parents' permission. Both parents much agree on the situation.
No, legally a minor has no choice in the matter.
No. If someone wants custody of you they need to petition the court but the court will not take you away from parents that are fit.
you need both of the parents to agree to have their child's last name changed
The court care about what is in the best interest of the children and just because one parents had an affair does not mean they are unfit to parent. It can be shared custody or one get it. The court wants the children to have access to both parents. The affair will not be the thing that decides custody.
Your sister will need to be appointed by the appropriate court. With your parents' consent it should go fairly easily.
Once a child is in state custody I don't think the mother has a say in who adopts the child. However, you may be allowed to meet the adoptive parents.
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Of course. If you are the one who has custody of him, then it really wouldn't matter whether or not you could find the father; only you can sign the papers of consent.