I have two Ts- one that I've been seeing for a long time, who I consider my "real T" and another that I see at our local Indian Walk-In Center because I went there looking to talk to someone about Native American beliefs (he's also a medicine man).
Anyway, "real" T... She has hugged me every session from the very beginning, and I love it. After about 5 years of therapy, I still look forward to her hugs at the end of every session

My first session, I had shared some difficult stuff (I had known her for about two years previously as a professor, and felt comfortable with her) and at the end she said "Do you accept hugs from professors?" I couldn't believe she was offering me a hug, but I was sooo grateful because I really needed one. After that, it's just always seemed natural for us to hug. Sometimes I ask her for one, but most of the time it's just assumed. I feel that it's helped me build trust and attachment. It has also helped me because in the past I have often felt untouchable, like there was something wrong with me. I think the world of my T, and before I would have believed that someone as "good" as her wouldn't ever want to touch someone like me. T has helped me get over that feeling. A few times when processing early traumas, I've gotten very scared and overwhelmed, and she has sat with me on the floor and held me, and played with my hair. I wish I had the guts to ask her to do that more. I felt so cared for, and so so safe. It wasn't until I'd known her for many years, so it felt natural and appropriate to me.
Other T is male. I've known him for a few months now. He is very physically affectionate... and I get uncomfortable about that. Lately I think he has picked up on that, because he hasn't been touchy-feely. He often offers me a hug at the end of the session, which I do like. But he's also held my hand and rubbed my legs, which I don't like. I have a low tolerance for physical touch sometimes. I think he's finally picking up on that, because he's keeping more distance.