I certainly felt obsessed in some periods of my therapy experiences. Part of it for me was that I am a very introspective and analytical person by default and the idea of doing that with someone else interested and knowledgeable can feel like the best of life for me. I would often have constant conversations in my head with the therapist and would want to discuss every thought with them. It can be very intense for me and can eat up a lot of mental energy. But similarly to what thesnowqueen said, it happens most often when my life is quite empty, unsatisfying otherwise and I substitute real life with the fantasies related to therapy. Also, I have a tendency to get into this kind of obsessional preoccupation and overthinking as a distraction strategy from what I really need to deal with, often practical things. For me it's not so much obsessing about the relationship with the therapist or the therapist himself, but wanting to dissect and discuss all sorts of things all the time. It was part of the process for me in a sense that therapy brought out my obsessional qualities and tendencies for distractions nicely. I would often jump all over the map in my interactions with the T when I was not willing to address the real important issues. I also just enjoyed being with the T and would look forward to it all week. Again, more intensely when I was otherwise quite isolated and having my social needs unmet.