Where Would I Be After a Brain Transplant?

The symptoms in some patients with uncontrollable epilepsy can be relieved by a severing the corpus callosum and thus separating the two hemispheres of the brain. A number of interesting experiments have been conducted in such patients which demonstrate that the two hemispheres each constitute separate, autonomously functioning brains.

But suppose that we could overcome the immunological and neurosurgical problems of transplanting one hemisphere of such a patient's brain into another person's skull after we had emptied his skull of its own brain. Then we would have hemisphere A still in person X where it started, and hemisphere B now in person Y in whom it had been transplanted. If I am person X, what would I experience after waking up from the operation? Would I sense myself and the location of my consciousness in my own original body as person X, or would I sense myself and see the world from my new body as person Y, where the other hemisphere of my brain now resided? Or would I become two consciousnesses?

The error here is that there would be no 'mind' superintending the consciousness of both hemispheres, since each hemisphere would now be a separate mind. Thus there would be no consciousness to be seeing the world from two different bodies and two different perspectives at the same time, but rather, just two different identities, one in each head. But would this amount to a duplication of myself, with my consciousness, roughly the same in each hemisphere of the brain, now in two different bodies?