Whether you are surrendering your child to adoptive parents, or signing off on your parental rights because your child's other parent has married and his new spouse wants to adopt her, the process is the same in New Jersey. You can do it in writing, or you can appear in court and do it verbally.
Make an appointment with a reputable attorney to discuss relinquishing your parental rights. Once you do so in New Jersey, the process is usually irrevocable. You can't change your mind. Make sure you have a full understanding of what you are doing and what it implies.
Consult with a counselor or therapist to discuss your decision. Be sure that this is really what you want to do. Try to separate yourself from whatever immediate situation is prompting you to give up your child. Circumstances change, and you may not feel this way five years from now.
Go online to the website for your county. Many New Jersey counties, such as Cumberland, provide legal forms free to the public. Download a "consent of natural parent" form. If your particular county does not offer forms on its website, visit the family court clerk in your county and ask for one. If you are relinquishing your child to his other parent, she may have an attorney who can draw up this form for your signature. If you are giving up your child for adoption, the adoption agency can also supply you with one.
Complete the form, giving your name and place of birth, whether you are your child's mother or father, and your child's name and where she was born. Explain the reason you are voluntarily surrendering your child. Give the names of the person or persons who will be adopting your child and explain why you have made this decision. Sign it in front of a notary. The form will include some language indicating that you "unreservedly and unconditionally" release your child to her adoptive parent or parents and that you are doing this of your own free will.
Give the completed, notarized form to the adoption agency, or to your child's other parent, if this is a stepparent adoption. Either one will file it with the court along with other documents finalizing the adoption process. Once this occurs, your parental rights are terminated and you do not have to take any other action.