Vista, did you have to make any modifications or can any P neck just drop in a Jazz body? Don't want to spend too much but I think this would help me like Jazz basses a little more.
JPee, I think all the 4 string necks and pockets are
supposed to be the same size
, or at least close
. I don't have a ton of experience swapping necks around, but this is what I have found.
Early in 2013 I bought 2 Mighty-Mite 1 5/8" (Fender licensed) Precision bass necks, a maple and a fret-less. The fret-less went on the CIJ Jazz, the maple onto a Squier Affinity P-bass. In both installations, the neck pocket in the bass body was a bit wider than the heel on the M-M neck and I made it up with a business card stuck with double sided tape (has worked fine for 2 years with zero problems), or wood veneer glued to the inside walls of the pocket.
Now here are the details and you'll see it's kind of hit or mis.
The M-M maple neck measured 2.5" at the widest point of the neck heel, the Affinity P neck measured 2.54" a difference of .040".
The M-M fret-less neck was 2.48", the MIJ Jazz neck was 2.5"a difference of .020".
Both basses had well fitting necks originally, and you can see that had I installed the maple neck on the Jazz it would have been a perfect fit.
The size of these necks as well as the pockets has been somewhat inconsistent. Making it up with shims along side the neck, as I did, is much easier than sanding a
too wide neck to fit, although I would prefer the latter as I could create a perfect fit. Gluing wood veneer to the side walls of the pocket is a good solution and I will use that method in the future, if done carefully it is nearly un noticeable.
I'm sure other brands of replacement necks have their quirks. Mighty-Mite has been a decent neck in all other areas of playability and adjust-ability.
To further muddy the waters regarding heel size, I have a 1969 Fender P neck which I have made two bodies for, the heel measures 2.475 on that neck. One of those bodies (solid Bubinga) will end up with the fret-less M-M neck eventually. I expect a nearly perfect fit with maybe a little neck sanding required.

Bottom line...expect to do some custom fitting, but you may get lucky and have a perfect fit.