Every state is different, but DMVs are the same all over! Coming from NJ to NC, we called the NJ DMV to ask what to do with the plates, and it was like this:
"Plates? what plates, we don't see no plates. Hey Gino, this faciabruto on the phone is asking what to do with his plates. Gino says yous guys no want to be talking about any plates. I swear on the virgin mary, dont call back!"
So we kept the NJ plates.
Now leaving NC, my daughter relocated to the socialist republic of Kalifornia, and there they have a whole cottage industry of companies that, for a fee, will do all the work for you and deal with the DMVs. I gladly paid $400 for them to do it all, returned old plates, insurance, inspections, stickers, more stickers, etc. Took a day and we ended up with everything done, no lines, no bullsheet.