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Old English ofer "beyond, above, upon, in, across, past; on high," from Proto-Germanic *uberi (cf. Old Saxon obar, Old Frisian over, Old Norse yfir, Old High German ubar, German über, Gothic ufar "over, above"), from PIE *uper (see super-). As an adjective from Old English uffera. As an adverb from late Old English. Sense of "finished" is attested from late 14c. Meaning "recovered from" is from 1929. In radio communication, used to indicate the speaker has finished speaking (1926). Adjective phrase over-the-counter is attested from 1875, originally of stocks and shares.
word-forming element meaning "above; highest; across; too much; above normal; outer," from Old English ofer (see over). Over and its Germanic relations were widely used as prefixes, and sometimes could be used with negative force, though this is rare in Modern English. Cf. Gothic ufarmunnon "to forget," ufar-swaran "to swear falsely;" Old English ofercræft "fraud."