This is my understanding.
Towing companies have contracts with the cities. These tenders come up every couple years or so and the various companies will bid for the contract. Usually they spread these contracts across multiple companies based on police divisions. This determines who tows your vehicle and where it's going to go.
Police will notify the registered owner (which isn't necessarily the person driving) that their vehicle has been seized.
The owner will be required to attend the relevant police division with identification where they will receive an authorized release form. If they can't verify you as the owner, they'll deny you your form.
You'll need this form to pick up your vehicle from the designated tow yard. No form, no car.