" Bringing Out The Dead " episode reaction posts from the SBH and look at what they had to say about that:

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Christina: WORD. Anyway, so Damon was TOTES impressed by Elijahs handiwork (see what I did there?). After they spoke for a bit and Elijah left, the look Damon gave him was one of such respect and awe and admiration. I think this might be the point where Damon realizes who he wants to be — he wants to be Elijah. Or like him. Last week he said that Elena wants him to be a better man, but if he does that, he’s scared he wouldn’t be himself anymore. I think Elijah is the next place he’s going to turn.
Cat: Damon could find far worse role models than Elijah. Imagine them roaming the Earth together….*sigh*
Cin: That’s the show I want to watch for serious.
Mel: I don’t think I’ve ever been more excited to see Elijah! He seriously was a BAMF last night! So fantastic. Christina, I totes agree with you on Damon wanting to be like Elijah. Its the perfect way for him to go. I mean seriously, who wouldn’t want to be like him? He’s just all kinds of awesome.
Cin: That is exactly how Damon wants to be. Screw this changing for people. Damon wants to go to Elijah’s College of BAMF-ittude and get a PhD in Pwnage. And by damned, he should have that dream come true! He is so very worth it. Gotta say though, that little moment with Elijah at the tea was probably one of the stupiest things we have ever seen Damon do. Was that his way of whipping his dick out? He’s already seen Elijah survive a coatrack to the heart and perform the infamous double heart rip, does he really think he needs to be getting all up in his grill? *tsk tsk*
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Now, Stefan got to have his bromance with Klaus, so why can't Damon have one with Elijah? :D