I've seen a ton of basses that are essentially a P bass body with a Jazz bass neck, but what I have GAS for is the opposite. I've always preferred the wider fingerboard of the P bass neck, but I love the versatility that you get with two jazz pickups since the P bass pickup is sort of a one trick pony, and blending different levels of the two pickups in a Jazz bass lets you cover a lot more ground sonically.
Fender makes/has made P basses with J necks, but I don't recall any Js with a P neck.
That said, I'm about 99% sure the necks are interchangeable, so you could pull a neck off a P bass and install it on the J, or order an aftermarket P neck for your J.
