In which type of relationship is it appropriate for someone to this message at the end of a letter/ email?
It depends on the person's personality and cultural background. For me, as a generalization:
Used by a man: for family, for romance
Used by a woman: family, romance, friends

I think a more common form is for Tom to write 'Love, Tom'

Best wishes (but not love),
Your signature came in right on the beat, MrM!
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thank you for your input,
personally, since english is my second language I would not have used that expression.
I may be using this site backwards from most people: trying to decrypt what a "real british"person has told me


catherine ( the "guest" from before of course)
You cannot guarantee that this Briton is in love with you Cath. Love,..... is a common way to write to a friend (though 'love to you' would usually only appear as part of a longer phrase).

I hope that doesn't make you sad!
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Hi Cath-- welcome to English Forums. Yes indeed, sometimes males writing females or vice versa (and otherwise) can intentionally or unintentionally appear over-fond for the circumstances.
 MrPedantic's reply was promoted to an answer.