Yes. For example the relation Trump apparently has to that king is that he has a great-to-something-like-the-32nd-power grandfather that a ton of people also have. What would it take to NOT have ancestors in common? If the family tree roots simply spread out wider and wider every generation, four grandparents, eight grandparents, 16 great-grandparents and so on? Well then when it comes to great-to-the-32 grandparents, one would have eight times 2 to the 32 (or maybe to the 31, not sure) of them. 2 to the 10 is 1024, 2 to the 20th is somewhat over a million, 2 to the 32 is over 4 billion. Multiply that by the 8, and there would be 32 billion of these grandparents alive at the same time to make that generation. I'd have my set of 32 billion of these ancestors, you'd have your set, so would the next person, and so on. That's what it would take to not have ancestors in common when going back so many centuries. But numerous websites think it's a "blood conspiracy."