Kenny, can you tell us how the PT model works - what the prices are etc?
Short answer is, "it depends". There's no one specific model.
In a lot of gyms, the gym itself controls the model. They will tell you what to charge, and they will take a cut. They will also basically give you sales targets, too. One example is Virgin - It's about £45 per session (depending on how you book them i.e single or multiple sessions), the trainer gets about £15 of that, plus aggressive sales targets to meet. I think that's right, anyway, it was a while ago I heard this from trainers who used to work there. However this kind of model is quite common.
What I love about my gym is, it's a fixed rent. You pay your rent and do what you want. You only get bothered if you don't make the rent. Everything above the rent is a profit. The only other fee is a yearly licence fee which includes insurance and registration on the exercise register (REPs). So, I could charge £5 per session if I chose to, or £50 per session. I like my gym because they don't care what you charge, how you charge it, and similarly, they don't care how you train people, so there's no silly things like bans on dead lifts or whatever.
Right now, I charge from 20-25 per session. Normally 20. Generally, a single session costs more but, if you book a "block", you decrease it by £5 each session - this is pretty much a standard in my gym, so members expect it because it's common place, too. It's like an unspoken model, really. The most successful trainer in my gym charges 30-35 per session. He doesn't do free sessions OR single sessions. You book a block, pay in advance, or don't book him at all. This guy is brilliant, to be honest. He put his prices UP when the recession hit. Other trainers bitched and moaned but I had nothing but respect for him. This is how he values his own service. He's almost arrogant when you speak to him i.e. he just believes this is what he is worth. It works for him, too.