You can find the Georgian Bagrations here. http://www.angelfire.com/realm/gotha/gotha/bagration.html
The first line used to live in Spain; many still do.
Pr.Irakli, the head of the house even married a spanish Infanta.
His son Pr.George (d.2008) was a famous automobile champion.
His elder son does seem very interested in the family claim and it's his younger brother who took the claim and married the heiress of the younger rival branch trying to reunite the family.
Unfortunately, as pointed out, the couple didn┤t last long and divorced, having had a son.
Pr.Irakli's sister, Pss Leonida, married GDk Vladimir Romanov and they were GDss Maria's parents.
You should take a look at https://www.royalark.net/
as this site will help answer some of your questions about Georgia and some other families.
The current Head of the Ottoman Family now lives in Istanbul. He was living in Lebanon, I think, and was evacuated on the orders of the current Turkish President when things got bad there. Members of the Ottoman family are still active in Turkey.
The newsgroup Royal Forums (https://www.theroyalforums.com/) has a page on the current activities of the Ottoman family.
There are two main branches of the Georgian Royal Family and both were united through a marriage of the head of one branch and the daughter of another. Their child will be the eventual heir of all the lines. Sadly, the marriage did not last very long. The family still live in Georgia. Their complicated genealogy can also be found on the site I referred to above.
Hope this helps.
Of the Turkish Empire which was abolished in the 1920s, what happened to the royal family? Do any survive? Are there royal decendents of what had been the Byzantine Empire in Constantinople? Are there members of the royal family of the former independent Kingdom of Georgia?