Final answer:
Overrunning on the cold side of a warm or stationary front generally leads to a gradually thickening deck of stratiform clouds caused by the lifting of warm, moist air over cooler air.
Step-by-step explanation:
When warm air overruns the cold side of a warm front or a stationary front, it typically results in a gradually thickening deck of stratiform clouds. This happens because the warm, moist air is lifted over the cooler, denser air, leading to condensation and cloud formation as the air rises and cools.
The gradual lifting process means the cloud deck tends to be widespread and produces steady precipitation over a larger area, as opposed to the towering, more localized cumulus clouds formed by vertical convection.