Ok, I'm going to try and get my current project migrated over to using JME. But first, I was wondering, how does jME's boundingbox (or sphere) work? I require some fairly accurate collision detection schemes. My current homegrown engine breaks the models down into multiple spheres and then tests on each sphere when the object is tested. Does jME do something like that? Or is the box and sphere just a simple bounding box or sphere around the entire model?
A bounding box or sphere is always a single shape. If you split your geometry up into different pieces ("batches"), you can have seperate boundings for each piece though (this is a relativly new feature). If you use SimpleGame, just press "B" and you'll actually see the boundings.
Aside from boundings however, jME can also do triangle accurate collisions. That means when you have two boundings intersect, you can have jME check if there are actually any intersecting triangles…
Ok… how do you do the triangle intersection test? 
(llama, you're following me around the forum, aren't you?) 
look at the tests in jmetest.intersection (there's tests for a lot of classes, consider that a form of documentation). There's one test that does model loading that's undergoing some changes in CVS at the moment (doesn't work here), but the other tests should be fine.