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Underbelly Elixir is looted from Underbelly Elixir in the underbelly of Dalaran, a.k.a. the sewers.  It randomly chooses one of three possible spells to apply to your character when it is consumed.

•  Underbelly Elixir - turns character into a tuskarr, fishing skill increased by 50
•  Underbelly Elixir - turns character into a wasp, allowing the player to fly in Dalaran even indoors.  (Was more entertaining/useful prior to the removal of the no-player-flight restriction in Dalaran.)
•  Underbelly Elixir - everyone becomes a mage.  NPCs, characters.  The least useful, but the most amusing.

The buff is only while in Dalaran.   Leaving the zone will cancel the aura.