The servers that are currently in use will be upgraded to TBC servers. Start the new Vanilla versions of these servers. You get the WOW TBC Gold choice of activating your character on the TBC server or the Vanilla version. If you wish to activate the identical character on both servers, you pay.
EDIT: This post was sourced from Blizz. "On patch day, you'll be able to launch the Battle.net desktop app and choose which game you want to play, either Burning Crusade Classic or WoW Classic. Your existing characters will show on both types of games under the name of your previous realm. After choosing a game, select a character you'd like to play and then confirm. You can use an optional paid service to gain access to the cheap Burning Crusade Classic Gold cloned character in both game types if you decide to play as your character on both. All you need to do is sign in your account as usual and play.