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Some headcannons about Tim Drake-Wayne (a reblog chain?):
The first time Damian hugs tim, he just fucking sobs.
Tim could count the number of times he got any physical affection from his parents on one hand (90% of that was all for the press), and as much as he would love it for affection to be normal in his new family, Dick is the only one forgoing with affection in the bat family.
So obviously Tim ends up touch-starved & seeing physical affection as ultimate trust.
So logically when the brother who hated you & tried to kill you the most out of all your brothers hugs you (which basically translates to 'I love you'), what else are you to do other than ugly sob for hours?
(Might add bat family's reactions to this post later)