grammar - Should I use "me" or "mine"?

I have the tendency to equate "mine" as something like "hers" and "his". But I am not sure if this is correct. I know I could say:

This pencil belongs to his.

But which of the following is correct if I say this:

This pencil belongs to me.

or

This pencil belongs to mine?

Which is correct? Should I use "me" or use "mine"?

Answer

The following are correct.

This pencil belongs to him. / This pencil belongs to me.

This pencil is his. / This pencil is mine.

This is his pencil. / This is my pencil.

The following are wrong.

*This pencil belongs to his. / *This pencil belongs to my.

*This pencil belongs to his. / *This pencil belongs to mine.