to cover something with saliva or slobber, or to drool excessively over something.
From be- (prefix) + slaver (from Old Norse sláfr or related to slime). This combines the intensive prefix with a word meaning to slobber or produce saliva.
Slaver, slobber, and slavering all describe drooling—and a slaver was also a ship involved in the slave trade, which shows how one word can have completely different meanings that have nothing to do with each other.
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