George XII, sometimes known as George XIII, of the House of Bagrationi, was the last king of Georgia (Kingdom of Kartli and Kakheti) from 1798 until his death in 1800.
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In 1942 Prince Irakli Bagrationi-Mukhraneli, of the genealogically senior branch of the dynasty, proclaimed himself Head of the Royal House of Georgia, in the absence of evidence that Bagrationis of the Kakhetian branch (which had reigned until 1801) still survived in the Soviet Union.
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Prince Nugzar Petrovich Bagration-Gruzinski is the most senior, known patrilineal descendant of Georgia's last king, George XII and is, as such, head of the Kakhetian branch of the dynasty which, although genealogically junior to the Mukhranelis, has reigned more recently, not having lost the throne of Georgia until 1800.

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Prince Nugzar's daughter, Princess Anna, married Prince David Bagrationi-Mukhraneli, on 8 February 2009 at the Tbilisi Sameba Cathedral. The marriage united the Gruzinsky and Mukhrani branches of the Georgian royal family, and drew a crowd of 3,000 spectators, officials, and foreign diplomats, as well as extensive coverage by the Georgian media.

The dynastic significance of the wedding lay in the fact that, amidst the turmoil in political partisanship that has roiled Georgia since its independence in 1991, Patriarch Ilia II of Georgia publicly called for restoration of the monarchy as a path toward national unity in October 2007.

Although this led some politicians and parties to entertain the notion of a Georgian constitutional monarchy, competition arose among the old dynasty's princes and supporters, as historians and jurists debated which Bagrationi has the strongest hereditary right to a throne that has been vacant for two centuries. Although some Georgian monarchists support the Gruzinsky branch's claim, others support that of the re-patriated Mukhrani branch.

[link to en.wikipedia.org]