[Not a reply to the message(s) immediately above, especially the non-ninjaing ninja-like one that's just popped up. Just making a general comment.]
Bear in mind that if you very strictly wish both parents to be previously unrelated, and thus all four grandparents to be previously unrelated, and thus all eight great-grandparents to be previously unrelated, and thus...
Well, eventually you're going to have some relations, once you're far enough past DF's "year zero" creation of separate individuals and have had a number of generations of pairing-off. The only non-relations you're going to be getting, eventually, are those who would never (by dint of racial or geographic separation) would never get to hook-up in the first place.
And cousins, as has been mentioned, covers
every common-ancestry relationship not already covered by the more immediate terminology, where there is at least one distinct generation between the shared root and each individuals sitting at the end of their respective family-tree branches. (With "Nth cousin, M times removed" nomenclature, as necessary.)
Frexample: Obama's famous eighth cousin in Ireland, and Sarah Palin and Rush Limbaugh who are both 10th cousins. 'Dubya' himself is an
11th cousin of Obama. My cursory searches don't reveal any "removed" value for any of these. But I did find that Obama and
Warren Buffet are apparently a mere
7th cousins, three times removed.
I, myself, have a 'proper' cousin (1st cousin, no times removed) who by dint of the efforts (or otherwise) of the respective siblings in the previous generation, in raising their families at different speeds, is significantly older than me. In fact his
son (a once-removed cousin of mine) is near-as-makes-no-difference the same age as me. (I think I described that correctly... I'm sure someone will pick me up if I've erred in some way.
) And I see no reason why any of my descendants (after another generation or two) couldn't 'mix it' with descendants of that branch. Given my side of the family's own tardiness in procreation that side is already full two generations ahead of my side! (This also means that there'd be a lot of unrelated DNA in their mix by that time that would make in-breeding effectively non-existent, even if my side still retains an 'excessive' 8th/16th/32nd part of the common ancestry's genetics that
might have clashed with that side's 'hand-me-down' genomes.)
I'm also tempted to link to the "All You Zombies" tale, just for the interesting family
tree pretzel-loop.