King of Qarth

"The proud Qartheen shook off the yoke of unjust Kings long ago... so they are told at festivals by the Pureborn, the Kings' direct descendants who have control of the Thirteen ever since. Only now instead of scepters they use ships."

- Xaro Xhoan Daxos

King of Qarth is a defunct title held by the ruler of the city of Qarth. Long ago the Qartheen rebelled against the King, and Qarth has been an oligarchy ever since.

The Pureborn are the descendants of the Kings of Qarth. They remain thanks to their hereditary seats at the Thirteen, the city's ruling council.

Season 2
Xaro Xhoan Daxos, a merchant from the Summer Isles and member of the Thirteen, conspires with Pyat Pree of the Warlocks to eliminate all the members of the Thirteen to crown himself King of Qarth in exchange for Daxos' aid in stealing the dragons of Daenerys Targaryen. "A Man Without Honor"/

In the books
In the A Song of Ice and Fire books it is mentioned that Qarth was once a monarchy, though it is unknown how the rule of the city passed from the Kings and Queens to the Pureborn.