You can always surrender your right to visit a child, or have parental decision making authority with regard to a child. You can "surrender" or agree to have your parental rights terminated if a step-parent or other family member wishes to adopt the child. You cannot simply "surrender" your obligation to pay child support for a child, as the right to receive support is not a right a parent can legally waive. Many parties enter into agreements of this type where child support is "waived", but be careful, as Florida case law has consistently held these types of agreements legally unenforceable. With the other parents consent, you can have your parental rights and obligations terminated, but that would require the consent of the other parent, and action by the other parent (i.e. the filing of a legal action) to have that occur.