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NJ Statute 9:6-1
Abandonment of a child shall consist in any of the following acts by anyone having the custody or control of the child: (a) willfully forsaking a child; (b) failing to care for and keep the control and custody of a child so that the child shall be exposed to physical or moral risk without proper and sufficient protection; (c) failing to care for and keep the control and custody of a child so that the child shall be liable to be supported and maintained at the expense of the public, or by child caring societies or private persons not legally chargeable with its or their care, custody and control.
The general rule is 1 year, although no specific time frame is stated in the statute.