I am looking for a single word to describe a one-sided friendship.
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By one-sided friendship do you mean that a person wants to become a friend of another person's but is rejected as they do not hold mutual affection? If yes, then that is not a friendship at all.
You can say that the person has admiration (or respect) for the other but they are not friends. Or the person trusts the other and is friendly to him/her but there is no mutual affection between them.
Not sure if this fits in well, but I thought you could consider unilateral, too.