Star Trek has been inconsistent on the issue. After all, if they are actually transporting the matter (vs. data only and making a new copy), then how do you end up with duplicates from the same beam at all? You've doubled the matter somehow.
The Physics of Star Trek (by Lawrence Krauss) is an interesting read, but it also does a good job of pointing out inconsistencies.
But the whole this (if it actually does make a "new" you is basically a modification of "The Ship of Theseus" paradox.