The Right of Annulment is the right to purge a Circle of Magi that is ruled irredeemable entirely by ordering the templars to kill all the mages in this Circle. Divine Galatea first granted it to all the Grand Clerics of the Chantry in 2:83 Glory. However, if there is no Grand Cleric and no immediate successor in evidence, a Knight-Commander of the templars has legal authority to use the right. 
By the beginning of the Fifth Blight the right has been invoked 17 times. Three more Circles were annulled between 8:30 and 8:40 Dragon.