ajobbins: Private companies cannot fine you, they are only allowed to demand liquidated damages (That is the actual financial loss they suffered directly from your actions).
I would have to disagree on this. If you park in a private carpark then you enter into a contract with the carpark owner.
If that contract says you must pay a penalty fee if you overstay, then you agree to that by parking there. Even if you are the only car in the entire carpark and thus they suffered no financial loss.