Assign

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Middle English: from Old French asigner, assiner, from Latin assignare, from ad- ‘to’ + signare ‘to sign’.

wiktionary

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From Middle English assignen, from Old French assigner, asigner, from Latin assignō, from ad- + signō(“mark, sign”).

etymonline

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assign (v.)

c. 1300, "to transfer, convey, bequeath (property); appoint (to someone a task to be done); order, direct (someone to do something); fix, settle, determine; appoint or set (a time); indicate, point out," from Old French assigner "assign, set (a date, etc.); appoint legally; allot" (13c.), from Latin assignare/adsignare "to mark out, to allot by sign, assign, award," from ad "to" (see ad-) + signare "make a sign," from signum "identifying mark, sign" (see sign (n.)). Its original use was in legal transfers of personal property. Related: Assigned; assigning.