If Aragon and Eowyn were indeed related, their relation would be too distant that they could hardly be called relatives [img]smilies/biggrin.gif[/img] At least, it's not as obvious as Aragorn's blood relation to Arwen where there was direct descendance.
By the way...
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Thus, it seems that Aragorn had to choose between two distant cousins.
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I believe Aragorn never really conveyed any affection or axcessive attention toward Eowyn. It was as if his love was fixed solely on Arwen and he didn't have to "choose" - there wasn't any love triangle (according to the books, at least; it was probably just included in the movie for effect or something... this topic is about "books", right?).