3.5nd dnd – Attack of Opportunity

We recently had a question in my party about when you can launch an opportunity attack. A group thinks you are only threatening the squares when you have arrived in the order of initiative for that turn, and therefore, do not threaten the squares and can not make any opportunity attacks before your turn. The other group thinks you can make an opportunity attack if someone leaves your threatened square (one per lap unless otherwise noted) before or after your turn. Who is right?