NOT A TEACHER.
You've asked an interesting question. I'd say that "a friend of mine," "a fan of John Lennon," and "a fan of the New York Yankees" are all correct.
Let's wait and see what a teacher has to say.

Student or Learner
Dear all,
I realized I haven't leaned a basic rule about the use of possessive " 's".
In the pais below, I think As are correct.
A: a friend of mine
B: a friend of me
A: a fan of John Lennon's
B: a fan of John lennon
A: a fan of the New York Yankees'
B: a fan of the New York Yankees
However, I sometimes see expressions such as "I'm a big fan of the Beatles", not the Beatles'.
Are Bs also fine actually?
Thank you
OP
Last edited by optimistic pessimist; 15-Jun-2010 at 09:31.
NOT A TEACHER.
You've asked an interesting question. I'd say that "a friend of mine," "a fan of John Lennon," and "a fan of the New York Yankees" are all correct.
Let's wait and see what a teacher has to say.
I agree- when the 'of' marks possession (this is an observation, not a rule I'm citing), the possessive is right: you actually have friends, ideas, toothpicks...
- so "an idea of his".
But 'fan of' doesn't refer to possession (at least, not unless 'possession' is the sort of possession that involves devils!)
I'd welcome some views from other teachers though...
b
***** NOT A TEACHER *****
Hello, OP.
(1) I was fascinated by your question, and I wanted to know the
answer, too.
(2) I googled yesterday and today, and finally found a great answer
(at least in my opinion) written by someone who calls himself "CalifJim,"
who answers questions at a forum similar to usingenglish. com.
(3) If I understood him correctly, here is the explanation that I have
been looking for (some of the following was NOT in his post; HIS words
will be in quotation marks):
(a) Good English:
I am one of John Lennon's fans.
I am a fan of John Lennon.
I am a fan of his.
(NEVER: I am a fan of him. )
(b) I am a fan of John Lennon's.
(i) This is NOT "bad" English.
(ii) It is the "meaning" ["not by rules of grammar"] that "cause
us to select the version without the 's more often" than we
choose the version in (b).
(iii) Mr. CalifJim then says that a sentence such as in (b) "is
too intimate ... because it implies (or nearly so) that [John Lennon]
personally knows you and counts you personally among his fans."
***** Thank you *****