It depends on the state you live, if your state considers a mobile home real estate becuase it has a "hud number" then taxes are paid on the home and charges to the owner of the park on the lot. If your state considers it a vehicle and not real estate, you may then not have to pay real estate tax but a registration fee. Other states break it down if it is on a foundation or is anchored or even if the axel is removed. Check with your local agent who can update you on what is and is not taxed.
They would pay property taxes if they own the lot (land), otherwise if they are paying rental space for the lot the landlord would pay the property taxes and they would pay personal property tax on the housing unit, similar to the DMV license on a car.