New Zealand Law
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It would be very difficult to avoid liability for the child support and this could only happen if the child was adopted by another person. There is no process to repudiate a child, and so unfortunately you are stuck with the child support. You can challenge the amount if you are struggling however and ask fr the amounts to be reduced particularly when you have no contact with the child. You would need to ask for a review through IRD for the amount.
Its abit late for a phone call but we can talk in the morning if you want.
You can apply for contact-perhaps what may be a plan is to suggest you tell them you will either start the process for contact, or if they dont want you in the childs life, suggest adoption. They may want to keep up the child support however, but they will need to consider you having involvement with the child, or losing the child support if they adopt