offshoot (n.)

by c. 1200 as an emphatic form of Old English of (see of), employed in the adverbial use of that word. The prepositional meaning "away from" and the adjectival sense of "farther" were not firmly fixed in this variant until 17c., but once they were they left the original of with the transferred and weakened senses of the word. Meaning "not working" is from 1861.

Off the cuff "extemporaneously, without preparation" (1938) is from the notion of speaking from notes written in haste on one's shirt cuffs. In reference to clothing, off the rack (adj.) "not tailored, not made to individual requirements, ready-made" is by 1963, on the notion of buying it from the rack of a clothing store; off the record "not to be publicly disclosed" is from 1933; off the wall "crazy" is 1968, probably from the notion of a lunatic "bouncing off the walls" or else in reference to carom shots in squash, handball, etc.

Old English sceotan "to hurl missiles, cast; strike, hit, push; run, rush; send forth swiftly; wound with missiles" (class II strong verb; past tense sceat, past participle scoten), from Proto-Germanic *skeutanan (source also of Old Saxon skiotan, Old Norse skjota "to shoot with (a weapon); shoot, launch, push, shove quickly," Old Frisian skiata, Middle Dutch skieten, Dutch schieten, Old High German skiozan, German schießen), from PIE root *skeud- "to shoot, chase, throw."

In reference to pool playing, from 1926. Meaning "to strive (for)" is from 1967, American English. Sense of "descend (a river) quickly" is from 1610s. Meaning "to inject by means of a hypodermic needle" is attested from 1914. Meaning "photograph" (especially a movie) is from 1890. As an interjection, an arbitrary euphemistic alteration of shit, it is recorded from 1934.

Shoot the breeze "chat" is attested by 1938 (as shooting the breeze), perhaps originally U.S. military slang. Shoot-'em-up (adj.) in reference to violent entertainment (Western movies, etc.) is from 1942. Shoot to kill is attested from 1867. Shoot the cat "to vomit" is from 1785. To shoot the moon originally meant "depart by night with ones goods to escape back rent" (c. 1823).

O, 'tis cash makes such crowds to the gin shops roam,

And 'tis cash often causes a rumpus at home ;

'Tis when short of cash people oft shoot the moon ;

And 'tis cash always keeps our pipes in tune.

Cash! cash! &c.

["The Melodist and Mirthful Olio, An Elegant Collection of the Most Popular Songs," vol. IV, London, 1829]