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late 15c., "to behave," from Old French deporter "behave" (12c.), from de- "thoroughly, formally" + porter "to carry, bear oneself" (see port (n.3)). Original sense preserved in deportment.
Meaning "banish" is first recorded 1640s, from Modern French déporter, from Latin deportare "carry off, transport, banish, exile," from de- in its sense of "off, away" + portare "to carry" (but associated by folk etymology with portus "harbor"). "The two branches are treated by Darmesteter as historically distinct words in French" [OED]. Related: Deported; deporting.