1)I was taught to use " of mine", "of his"," of hers"
Ex:The book of mine is very interesting.
But I often see the way of using "of me" instead of"mine".
EX: piece of me_the name of Britney's Hit.
Therefore i'm wondering if both ways are correct. Please help me!


2)I have one more question.
If we must use "of theirs" instead of " of them", why do we use " of my friends" instead of " of my friends' ".
I think : theirs=my freinds' and them=friends.