Sorry, gonna have to be a bit crass here for clarity. Does half a pump work correctly, or half a filter? No. Hearts and kidneys are composed of discrete structures that work together as a biological machine. So transplanting a portion of one simply doesn’t work; also, while you can grow heart or kidney tissue, growing back fully-differentiated tissue structures is another matter entirely (though kidneys have been known to sometimes regrow a bit if inadvertently damaged when the owner is young), so even if you were to transplant such a partial organ, and it somehow managed to function, there no chance that said organ would completely regenerate, let alone regenerate correctly. The liver, by contrast, is effectively composed of a single undifferentiated (even though the organ itself structurally has lobes) tissue type, and, as such, can function correctly even as a small(er) piece when transplanted, and can also grow back in time.
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