Sometimes branches die out after a fork. Other times they replace the "official" branch--consider X.org vs. XFree86.
As for "bear[ing] the complete cost of development", that's just a matter of network effects. It could easily go either way, depending on which branch get more participation, and right now the balance appear to be in favor of LibreOffice. There is also the fact that anything added to Apache OpenOffice can be merged into LibreOffice, but not vice-versa.
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