The roaches overran our kitchen.
The Kudzu plant overruns more of the South each day.
The Crusaders overran much of the Holy Land.
WordNet 3.0 Sense Numbers: 1, 2, 4
NOTE: compare to sense 1, where the area filled is either geographical or political. Here is is a specific point in space or the confines of a container. Also, conquest is not involved.
The plane overran the runway.
Water overran the edges of the glass.
WordNet 3.0 Sense Numbers: 3, 5