Parking lot accidents are both confusing and can result in large disagreements between parties involved. There really are no set laws while in the parking lot of many malls and shopping centers, so when a parking lot collision occurs, many disagreements can result when dealing with fault. This is because parking lots, are generally private property so normal road laws do not fully apply.
In determining fault, the main indicator is how the accident occurred. If the collision occurs while someone is backing out of a stall, usually it is the person backing up who is at fault. The person reversing has the responsibility to yield to on-coming traffic. This will however differ, depending on the exact location of the impact. If a car backs into you, then they are almost always liable for the damage.
However, if you hit the car that is backing up, you may be found partially or fully liable. The further 'up' the collision occurs (closer to the front of the backing car) the more liability will be placed on the non-backing up car.
If you are involved in a parking lot collision, gather as much information as possible. Did his reverse lights come on? Did he honk before backing up (in reality who does? But this is what they teach you to do in driver's Ed.). Be sure to gather all witness reports, so that you can fully support your side of the story.
The majority of the time, one driver is usually never found fully liable in a parking lot accident. Fault is usually split between the parties, sometimes equally, sometimes not equally which is why it is very important to get as much information and witness reports as soon as possible. Additionally depending on the severity of the accident you will likely want to contact the police and your insurance company.