depends on the wording of the law.
For example, where I live (NJ), if you had a pre-ban ar-15, you couldn't bring it in. You could for a number of years provided you got a waiver form the police (which never happened unless you were a cop). The window for the waver closed though, so even that wouldn't cut it these days. You have to store it out of state, or get rid of it somehow. Theoretically, if the window was stillopen and you knew the right folks to get the waiver, you'd still have to leave the 30round magazines at home unless you rigged them to hold no more than 15 rounds.
However, with the new smartgun law, it's different. From the reading of it, transferring a handgun that isn't a smartgun is what is the criminal offense ofr the transferer or transferee. However, if you move in from out of state, no transfer occured within new jersey. You are just in posession, which since theres the grandfather clause for posession, seems to be cool. (BTW, big IANAL nor am I a weaselly corrupt new jersey supreme court judge goes with this reading). Also, currently inheritence of a firearm gets around a number of transfer rules, and is a muddy area. The legislature wants to make it so that inheritance is prohibited without a transfer, however you can feel their pain from many many miles away over not being able to legislate the lives of people in other states.