Grammar Rules: Any One vs Anyone

Any one vs Anyone: Two words or one? I used to confuse this a lot! Here are the rules:

Spell as one word when the accent is on any:

Anyone can use this room.
Almost anyone has access to her tv.
Can just anyone stop by?
When will anyone care?

Spell as two words when followed by of:

Any one of them can come.
Who will attend any one of the conferences?
Any one of the dogs can fight.
My mom could be any one of them.

Authors/writers: Make sure you're on my list of authors!