I think I'm understanding this better (now I've started having a drink, go figure).

Half of me, my conciousness would be in one body, the other half in the other body. There wouldn't be any connection between the two halfs, the conciousness in one half will think 'What has determined 'me' to jump into this body but not the other one?', and vise versa.

But you've got to be half of what you are, so maybe you would only be half as self aware as what you were if that makes any sense, as in you're more zombiefied.

I mean where does it stop and why, what about cutting one of the halfs into another half, then that half into half until you end up with an atom? Are atoms concious? Maybe, but the self awareness is so small that it's almost as though it doesn't exist.