My first T offered me a hug at the first session, but made it totally clear I could say no. I did say no. Periodically, he would ask about hugs and I just didn't want to be touched. At our last session together, he said, "are you really going to leave therapy without EVER giving me a hug? Think we could try a hug just to say goodbye?" So, I hugged him, and it was fine, and I regretted not hugging him more often.
With my current T, I was in therapy about a year and a half, I finally got around to talking about the sexual abuse. I really struggled after that session and the next session asked for help getting grounded before I left the session. My T asked me what I needed, and I asked him to touch me and then kinda freaked out because that sounded weird. He didn't take it in a freaky way, though, and immediately asked if he could hug me. He told me there had been many times he wanted to hug me, but his personal thing is that he only hugs if people ASK for a hug AND he thinks it's therapeutic.
And both T's hug in a whole body kinda way, which with my second T freaked me out a little. My first T was a gay man, and I had no real emotional issues about him. I liked him fine; in retrospect, I loved and still love him, but it's a "I'm very fond of him and very grateful" kind of love. With my current T, I swing between "I'm very grateful and fond of him" kind of love and "OH MY FREAKING GOD, I LOVE HIM!" kind of love.

So, the full body hug was wonderful and comforting but arousing. and it lasted longer than I anticipated, which added to the arousing thing.
Wait, what was the question? I'm all distracted now.