Water will run off a truly flat plate for the same reason it runs off the tennis ball. It's attracted to the Barycenter.
Water will remain in a dished or rimmed plate for the exact same reason. It can't flow over the rim, as long as the plane of the flat bottom of the plate is perpendicular to a line from the plate to the Barycenter. Tip the plate so that the bottom is out of perpendicular with that line, and the water will seek the Barycenter.
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