Our RB cat, Midnight, was Snowball's companion for 10 years. Snowball became the alpha when he was still a kitten, and kept that position the entire time the cats were together.
Here are just a few of the things we saw Snowball do as the alpha:
If Midnight was playing with one of their toys Snowball would take it away and then would play with it himself. If I was sitting in a chair with Snowball on my lap, Midnight wouldn't be able to approach me if he was staring at her. If Snowball looked away, then Midnight could approach me. If Midnight needed to use the litterbox, Snowball would follow and then just watch from a distance, and sometimes he would even try to prevent her from using the litterbox. Sometimes Snowball would make a very soft, low noise (not growling) that was directed at Midnight and she would move away. Also, Midnight was always the cat that moved away during any type of confirtation(sp?) between them. If Snowball stood sideways in front of Midnight and blocked her path, she couldn't walk around him, and would have to wait for him to leave before she could move forward again. And like Sammie5 mentioned, Snowball would seek out the highest perch.
Coco Maui, IMO the alpha cat controls the actives of all the other cats.