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BEVERLY HILLS, California — Judging by the photos that leaked Tuesday night, a lot of people enjoy dreaming that Robert Pattinson and Kristen Stewart’s onscreen romance also extends offscreen. But no matter what the truth is, this much is fact: Rob and Kristen are happy to have the other at their side as they ride the “Twilight Saga” wave.

“He’s thoughtful,” Stewart explained recently when we asked the actress to name the quality in RPattz that means the most to her. “I don’t want to be specific. It’s funny to talk about your friends in [these terms], because this is now going to be the one thing that’s my favorite thing about Rob. It’s going to be the thing.”

Way back in March 2008, when MTV visited the “Twilight” set, two things were obvious: Kristen and Rob were going to set the big screen on fire, and the duo were growing close. Onscreen, Edward and Bella are romantic, honest and protective of one another; offscreen, Rob and Kristen have a funny, self-deprecating dynamic that has helped them grapple with all the insanity of the saga’s explosion.

“It’s strange, because she’s changed over the movies I’ve done with her,” Rob said of his leading lady. “I think from the first one, I was so quiet [and] very determined to do something on the first movie. I wanted to look very serious, and it made her, I guess, a little bit more reticent about how to deal with me.”

These days, the duo fly around the world attending premieres and events, and all those hours together have undoubtedly made life easier than it would be if only one was experiencing all this fame alone. “He’s real,” Stewart said of Pattinson, arguing that he hadn’t changed — and that’s a good thing. “He’s a real guy.”

“As we’ve been doing stuff together,” Pattinson said of his favorite quality in Stewart, “I guess what I admire is that she’s more stubborn than me in a lot of ways. I mean, she really stands up for what she thinks is right and is generally on the same page with what I think is right.”

“[Rob] has gotten more confident as he’s gotten older,” Stewart said, explaining that although he’s still the same guy on the inside, he’s no longer the shy, giggling actor we first interviewed in Portland nearly two years ago. “Just as all of us have gotten to know ourselves a bit more, because we’re constantly put in a position of self-reflection. If you’re constantly asked about yourself all day long, it really makes you actually consider what you’re saying, and you’re in a position where people are listening.

“I’ve seen him grow a lot, and I’ve seen him get more comfortable with his position [as a celebrity],” Stewart added of Pattinson. “But I also don’t see any change in who he is.”