The Big Anti-Fairy Wand (much like the The Big Wand in Fairy World) is the source of all power in Anti-Fairy World. In the episode "Anti-Poof", Foop drained all of Anti-Fairy World's power from the Anti-Fairy Wand and used it to turn Anti-Fairy World into Care-Fairy World. It remained this way until Foop was defeated by his good counterpart Poof. Unlike the Big Wand, it looks rusty, gloomy, half broken and it is black, and being the complete opposite of the big wand, it's magic comes from non-belief in fairies.
Unlike Fairy World's Big Wand, there wasn't much concern about the loss of the Anti-Fairies' magic when it was destroyed by a giant rabid bunny in Fairly Odd Baby. Whether it did affect their magic or not is unknown.