So the brain can function normally without a whole half? That's very interesting. Now I'm wondering how much can be removed without adverse effects :-)
A non-precise answer: a surprisingly large amount if you're careful about which parts to remove and if you do it really, really early in life. ;)
In adults (or even adolescents) though, not as much luck.
In the case of hemispherectomies on Rasmussen's patients, you can analogize it as: people are dual-core by default. If you remove one of the cores early enough in life (like <5 yrs old), you can re-route the wiring so that processing can done by one of the cores, and still be pretty much normal. But whatever subtle thing is lost when if we don't do parallel processing like we usually do -- that things is pretty subtle to test for as well.