You can legally move out without your parents’ permission when you are 18 years old.  In Arizona, under A.R.S. § 8-201(3), "adult" means a person who is eighteen years of age or older. 

Until then, your parents are responsible for you and, under A.R.S. § 12-661, your actions.  If your parents know where you are, that you are with another responsible adult, and they allow you to stay there, they are “permitting” you to be there.  If, while you were there,  they do not provide reasonable support and maintain regular contact with you, including providing normal supervision, their actions may constitute abandonment.

Otherwise, you can try to become emancipated if you are 16 or 17 years old, which means that the courts will legally separate you from your parents.  You would assume most all of the responsibilities of an adult.  You would have to demonstrate that you can live independently and then the court would determine if that is in your best interest.  Your parents would have an opportunity to object during the court process.  For more information about the emancipation process, visit Laws - Emancipation on this site or you can view an Emancipation Informational Booklet from the Arizona Supreme Court Administrative Office of the Courts, Dependent Children's Division or you can visit the Emancipation of a Minor online information page.

Depending upon your home situation, you could try to seek help to improve your relationship with your parents. However, if you are trying to leave home due to an abusive situation, do not wait - call for immediate assistance:

-Arizona Child Protective Services 888-SOS-CHILD or 888-767-2445
-Child Help USA Hotline 800-422-4453
-National Crisis/Suicide Hotline 800-999-9999
-National Domestic Violence Hotline 800-799-7233
-Teen Link (Various Topics) 800-235-9678
-Youth Crisis Hotline 800-448-4663.