Thank you for entrusting me with your question. To rephrase, the question is how to initiate the process to get a custody order in New Jersey, and if mediation is an alternative to going through the court. I will start by saying that you should not rely on this information as advice or apply it to a specific situation without a more thorough consultation with counsel.
That said, this forms packet is designed for unmarried parents seeking child custody: http://www.judiciary.state.nj.us/prose/11492_fd_initial_appl_kit.pdf
Mediation is always possible in lieu of a contentious court case. The parties can mediate before or after starting a court case. However, any mediated agreement must be ordered by the court to be enforceable. So, if the parties want their mediated agreement to be enforceable, they would need to file for child custody anyway and just ask the court to adopt the agreement as an order.
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