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.
(..) of one betrayed by his father. I bid you... rise. Grover! Hands. Try not to cut them off. I'm pretty attached to them. I have to get to the Fleece. So, what are we supposed to do? Right. I know you can breathe under water, Jackson. (..)2013 Percy Jackson: Sea of Monsters