Auto Insurance Claims: Parking lot, south aisle, wheel image

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Hello I was involved in an accident within retail parking lot.  

Google map image -  

I was traveling in the west/east aisle heading west.  Other car was in the north/south aisle heading to exit parking lot north.  I was hit by the other car on the back part of my driver side.  Damages start toward end of my driver side door to the back driver quarter panel and back wheel (image attached). Other car damaged in the front bumper and hood.  Other car leaking fluid. What could determine "right of way" in this situation?  It is a private parking lot.

Parking lots are difficult when traffic controls (like a stop sign) are not obvious.  In general, the larger road/aisle is considered to have the right of way and side roads/aisles are expected to yield.  

Unfortunately, the other driver was on the larger and more delineated roadway, so it could be said he/she had more of the right of way.  However, since neither driver  had a stop sign, the argument could be made that both drivers should have exercised care.  Also, you were farther into the intersection as made clear by the damages (your side, his front) so he had a better chance to avoid you.  

In your state, you are barred from recovery if your negligence is 51% or more.  If less, you get a percentage of your damages from the other party.  Determining fault is not an exact science and different people could see this differently.  Best bet is to let your insurer fight it out with the other insurer.