I think that the result would be to turn one healthy person into 2 damaged versions of the same person. I think that you could even make the argument that we are all actually two people, who cooperate so intimately and have enough neurological connections that we have the illusion of unity. Rather like that single body/two heads twin mentioned, taken to it’s logical conclusion.
I’m suprised I haven’t heard about this before… it’s somewhat discomforting.
When they talk about interviewing the different halves of one man’s brain, it really does sound like they’re dealing with seperate conscious entities.
EDIT: Woah, seems like people are interpreting the OP in totally different ways.
I was imagining the scenario where you, say, swap the left hemispheres of two people: hybrid brains!
Oh, thanks for that link! I remember reading that Life profile on the Hensels long ago.
Its pretty freaky, but it hasn’t bothered me as much as it has some, because I’ve always thought each individual person consists in several individual consciousnesses anyway. 
-FrL-
After all how else can I explain all these voices in my head…
Since there is no factual answer… I believe what might happen should there be no complications from surgery itself, is that either half brain must be dominate. This is the brain that is utilizing the brain stem. If you add half a brain from another person minus the brain stem, the dominate brain will simply let the other half know who’s boss. Adding a second half would be like adding another hard disk to your PC; it may or may not contain an operating system, but will definitely use the extra storage. Or in this case, the dominate brain will tell the other half, “other half > format d:, you’re now my bitch”.
Could the OP please chime in and explain that he meant each of the two people after the surgery would have only half a brain?
-FrL-