Magical powers were once thought to 'be attached to' the stone. [=the stone was once thought to have magical powers]
Little credibility 'was attached to' his story. [=people did not think that his story was very credible]
The shy child 'attached' herself 'to' her mother [=stayed close to her mother] during the whole party.
(..) five minute headstart. You want that thing off your face?! Let's go! Of all the legs you had to shoot, that one was attached to his favorite. You don't have to do it just because he tells you. What choice does she have? / He's not gonna hurt us. He needs us. Why? / To bargain. (..)2015 Mad Max: Fury Road