Correct. As with possession of handguns, possession of hollow-points is GENERALLY PROHIBITED, and only legal by exemption. The specific statute:
2C:39-3f(1) - Prohibited weapons and devices - Dum-dum or body armor penetrating bullets
Any person, other than a law enforcement officer or persons engaged in activities pursuant to subsection f. of N.J.S.2C:39-6, who knowingly has in his possession any hollow nose or dumdum bullet [...] is guilty of a crime of the fourth degree
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So - that's our base line... possession of hollow nose bullets is illegal. If you are engaged in activities pursuant to 2C:39-6f (going to/from a range, to/from a place of hunting, or actually engaged in hunting), then possession is legal.
There is also a specific exemption in 2C:39-3g, stating:
Nothing in subsection f.(1) shall be construed to prevent a person from keeping such ammunition at his dwelling, premises or other land owned or possessed by him, or from carrying such ammunition from the place of purchase to said dwelling or land
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So - what does all this mean? It means... legal to purchase, and transport directly to your home. Legal to possess in your home. Legal to transport directly to/from a range. Legal to transport directly to/from a place of hunting. NOT legal to leave in your car while you go shopping.
I have no idea where the myth of, "it's only illegal during the commission of a crime" or, "it's just an add-on charge to another crime" came from. Clearly, from reading the statutes above, it's a stand-alone offense. Note, also - that the crime specifies "bullets" - not "ammunition". That means even a keychain made with an HP projectile (no power, no primer... not loaded ammo) is illegal.
Cone256 - it is not illegal to possess non-HP ammo anywhere. Driving around with a box of FMJ's in your trunk is perfectly fine. The only statute on possession of ammunition is the above, relating only to hollow-point ammunition.