There's nothing your mother can sign that will remove her legal obligation as your parent. You must go through a court and have a JUDGE determine that her obligation and authority over you is terminated. Having a history of being a runaway, as well as ANY type of criminal charge, whether based on truth or lies, is almost an automatic reason for a court to deny your petition, even IF you can show that you are fully capable of self support (the MAIN requirement of emancipation). Generally, parents are allowed to be mentally, verbally, and emotionally abusive. CPS is mostly concerned with whether you are being provided with shelter, reasonable clothing, a sanitary environment, enough food to eat, and are not being physically abused or in imminent danger of physical abuse or neglect. It is however a crime for your mother, if she is your legal guardian, to simply kick you out. You need to be calling the police and CPS when this happens. Keep in mind that while such a pattern of behavior from your mother MIGHT result in CPS removing you from her care, it will be totally up to THEM as far as were you'll go and where you'll live after removal - and will in NO way be a step towards "emancipation". Have you asked your grandmother to consider taking the steps to become your legal guardian, in light of your prior removal from your mother's care?