The Stuart claim to the throne seems to go to the present Duke in Bavaria, HRH Franz. Franz has no children, so his heir is Max, his brother. Max had only daughters, and the eldest is Princess Sophie of Leichtenstein, who is a Serene Highness of Leichtenstein, but also a HRH of Bavaria. Her heir is her eldest son Jospeh Wenzel. These people, however, make no claim to the throne of England. It is the "Jacobites" who make the claim for them.
Prince Joseph Wenzel of Leichtenstein was the first Jacobite heir to be born in England since the last ruler of the House of Stuart there since the Hanovers took over.
Of course, Electress Sophie of Hanover also had Stuart lineage, but these Jacobites have it all figured out that the correct descent is to the present "King of England," Duke Franz in Bavaria.
I became interested in these wandering genes through my own genetic history, which I didn't find out about until about 16 years ago, when I was diagnosed with Porphyria, a disease quite a few royal people have had or even have today. I knew nothing at all about my Scots antecedents, since my parents thought discussion of such things was vulgar. But I became aware that my Scots grandma came from Dundee (she was my porphyria link) and I could not trace her back more than four generations, none of them royal or noble or even rich.
But then I traced back the family roots to the era in the 12th century when my ancestor Robert Pollock lived next door to Walter Fitzallen, and apparently was FitzAllen's aide in Shropshire and then in Renfrewshire. Fitzallen's descenants become the Royal Stewarts. The Stuarts are well known in later centuries for having the Porphyria gene, which is very rare (at least in so far as those officially diagnosed). I probably got the gene from a Stuart or more directly from one of the lowland Scots families who married Stuarts over the years, including Leslies, Hamiltons, Pollocks, Maxwells, and so forth.
So I have no direct descent of royalty, but boy do I have a bloodline descent of Porphyria, not something one would choose. The mystery to me is how the gene got down those years to me. I now know my dad had it, and his mother and sisters and probably a couple of cousins, but I can't look back through the years to see how it got to me.
Do people other than royals have it? Of course, most do not even try to trace royal lineage, but it seems to be a disease which sprang up through inbreeding, and I know some of my Scots ancestors were champs at that, such as the Maxwells, who married cousins every time one was available (and sometimes abandoned the female spouse after an heir was produced, very bad people to be related to). Maybe this bad behavior produced a curse? I hope not. I have prayed for the curse to leave in any case.