jazz and presicion necks

As far as the neck pocket goes, I do believe they're the same size, so it should work. Jaco played a fretted Jazz bass with a Precision neck on it, and I know that Duck Dunn did it the opposite so he could get the fat sound and appease his tiny fingers. Dunno about off brands though.

 

I just put a MIM Fender Jazz bass neck on my MIM Fender P-Bass. It was a perfect fit and took about 20 minutes total.
The neck came pre-drilled for all screw holes.
I don't know about American made basses and necks but I would hope they'd interchange just as easily.

 

With any production parts there's always discrepencies, even between same/same necks and bodies. They may be off by a few thousands. What you don't want is a neck that's sloppy in the pocket. But I do think that the p-bass butt is about 1/16th larger in a general build. Some swap straight across. Some would need to be shaved those few thousandths to fit. Just try and get accurate actual measurements beforehand.

You'd be surprised at the high number of different manufacturer necks that fit into other body pockets. Even a loose fitting neck butt can be shimmed too. I've used brass shimstock on probably ten different necks that transfered tone very nicely.