I think the whole discussion doesn't lead anywhere. We're trying to bend the ideas of self, continuity and sameness to our quite limited imagination.
Let's take the teleportation example: my rebuilt self is just as much "me" as the original was (or still is, should the device keep it intact) -- all atoms are in exactly the same place, and what's crucial, the memories and mental characteristics are preserved. It's not my clone (where only the DNA is the same), it's the exact replica. Doesn't matter that it's built from freshly assembled atoms, since our bodies continuously assimilate new atoms and shed old ones anyway. In that we're more resembling a wave on the ocean than a Luke Skywalker's lightsaber prop, where it actually counts that it's the exact set of atoms that Mark Hamill wielded on set. If you care about memorabilia anyway.
The two existing duplicates of me are obviously not "the same me", but nobody should expect them to be. They both are a continuation of myself. Like the aforementioned wave, I'm not my atoms and their configuration, I'm the continuity of their ever-changing state.
.......
When a cell divides, does it cease to exist? If so, at which point exactly? Are the two newly created cells the same cell as the one that was there before? Are they a half-cell each, even though they both are full cells now? Is one of them the original cell that gave half of its matter to create an offspring? Would everything be back to normal if one of them ate the other one and we could say that the original cell just performed a crazy transformation, but it's still the same cell (the same atoms, chromosomes and all)?
These questions might seem reasonable, but I think they stem from our mistaken desire to qualify and label things. Still, the reality isn't limited to our understanding of it.