You take the exam on cars provided by either the examiner or your driving school.

The second option usually happens only if you wanna get an automatic-only car driving license (B78), like me. I had to pay my instructor for renting me his car for the exam’s duration – standard practice, especially since it was his “daily” after working hours.

If you’re super lucky you get to take it on the car you used the most while learning

If you want to get the full driving license (B) and have no disabilities, you learn on a driving school’s manual and take an exam on an examination center’s manual. They’re separate entities, so you never get the same physical car. At least the model should be the same – driving schools usually match their fleet with whichever model local examination center picked. E.g. in Warsaw it’s Hyundai i20, so most (if not all) schools teach on Hyundai i20.

depends how cars get allocated

Like I’ve said before, examination center’s cars are never used for teaching. That’s driving school’s job.