So... is Tanin no Kankei finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: October 21, 1994
Manga finished: July 01, 1993
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Tokiro Ehara, a professor envisioning an environment of eager young female students, takes a position at an elite girls' high school.
His expectations are challenged when he encounters Miyako, an unconventional and somewhat rebellious student, before his first day.
He believes it's his duty to guide her towards a more refined demeanor.
Miyako, however, has her own intentions and seems determined to test the boundaries of their student-teacher relationship.