I have never been very attached to my therapists as specific people, for me it was more all the analysis and talking about personal patterns that I found addictive. When I obsessed about therapy, it was much more a compulsive desire to dissect things and to discuss them and not the therapist's person that I would be preoccupied with. There was a very big difference though between my two Ts in terms of my respect and liking for them.

For me, what I call and experience as attachment can only develop and be sustained as a mutual state, with ~the same level of interest from both parties. I can feel intensely drawn to someone but it never lasts if it is not mutual and balanced. Interest and liking can last without mutual bonding for me but that does not usually involve strong desire to be with the person and missing them much when we are apart. Obsession can also last in a one-sided way, but I personally don't like to use the word "attachment" to those.

So I think there can be a big difference between healthy and insecure attachments, as some others pointed out. From what people tend to report on this forum, insecure attachment almost always comes with a lot of discomfort and pain and healthy attachment is a much more relaxed, positive experience, without much obsession. I think not only in therapy but also in everyday life.

Finally, I really don't think that therapy relationship and feelings for T always have something to do with parental feelings and desire for a caregiver, or whatever we lacked as children. Some therapy modalities push that concept, going even as far as claiming that even if a client is not in therapy because they seek a parental figure, at least unconsciously that is the case. I think that is pushing it too far and it can sometimes be used by the T as a defensive tactic, putting down the client's discomfort and criticisms to transference.

I did a lot of googling and online research on my Ts but for me it was a need for information and hopefully having a more realistic, complex picture about them, rather than a need to feel close to them. I rarely daydreamed about them and what it would be like to have a personal relationship with them - it happened sometimes, but very transiently. When I had those curiosities, it was usually just an interest to see who they are, independently of me and our relationship. When I thought about the relationship, usually it was in the context of professionalism - I wanted to have a decent professional relationship with them, and I either admired the T for good professional conduct or despised for failing at it. In this sense, if my T relationships was expected to model anything, it was most similar to work collaboration for me, not personal relationships (for which therapy is simply way too limited, IMO).