In my opinion, and feel free to counter argue, Vaati and Zant are the reincarnations of Ghirahim, the reasons i think this are:
1. All have similar appearances (Vaati and Ghirahim in particular)
2. They are all trying to revive Ganon/Ganondorf/
Demise (who are all incarnations of the same person)
3.And perhaps the "origin" of sorts for Ghirihim (or more correctly,
Demise's Master swordcould be the twilight realm, which could point towards a Zant/Ghirahim connection, but could debunk a Vaati conection because Vaati was originally a Minish.
What do you guys think?
