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Phrase(s): conk off [and] conk out
1. Sl. (from years ago.) to fall asleep. • I conked off about midnight. • I was so tired that I nearly conked off. • I was afraid I would conk out while I was driving. 2. Sl. (always conk out.) [for something] to break down; to quit running. • My car conked out finally. • I hope my computer doesn’t conk out.
McGrawhill's American Idioms And Phrasal Verbs