My t is very boundaried, and, as noted above, we are both British...
She keeps very good time, not offered hugs and just lightly touched me on the arm when I was really struggling. I can email if needed and I do sometimes, I could call in crisis but I haven't, and wouldn't.
Though I wanted hugs and much more contact initially, these boundaries have been good for me, and I am sure I have been able to get through ET much more quickly because of it.