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Dear Grammar Guru, It looks too difficult to search by myself, so please let me directly ask a question about the following usage. a A of B's

#1. She is a great fan of Tom (Cruise).
#2. She is a great fan of his.

Is #2. better than "She is his great fan."?

Why "She is a great fan of him" wrong?

A possessive pronoun follows "of", then why not "a fan of Tom's".
And is"She is Tom's great fan" all right? I think I understand the difference b/w "
She is my friend." and "She is a friend of mine." but why not "She is a friend of me."?

I've just found an example sentence in Oxford Advanced Learner's Dictionary.

"Can't you throw out that old bike of Tommy's?" Not "of Tommy".
But "the paintings of Monet" not "of Monet's".
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You cannot usually put a possessive before another determiner and a noun. We can say 'my' friend, 'Ann's' friend, 'a' friend, or 'that' friend, but not 'a my' friend or 'that Ann's' friend. Instead, we use a structure with 'of + possessive'.


DETERMINER + NOUN + OF + POSSESSIVE.

That policeman is 'a friend of mine'. How's 'that brother of yours?' 
I met 'another boyfriend of Lucy's' yesterday.
He's 'a cousin of the Queen's' She's 'a friend of my father's'
Have you heard 'this new idea of the boss's?'
My work is 'no business of yours'

The structure has a variant in which the noun does not have possessive 's:
this is sometimes used when talking about RELATIONSHIPS.

He's a cousin 'of the Queen'. She's a friend 'of my father'. 

I hope I've 'semi' answered your question!

Comments  
I'm creating a title for a monthly newspaper and I'm wondering what the difference in meanings these two titles have "The Catalyst Of Democracy" vs. "The Catalyst For Democracy"
Thanks for all your input.