The present participle of asterisk; the action of marking something with an asterisk.
From asterisk (noun), which comes from Greek asteriskos ('little star'), plus the gerund suffix -ing. As a verb, 'asterisk' became common in publishing and editing in the 20th century.
Asterisking is one of those verbs that only exist because of punctuation—like exclaiming or parenthesizing. It's proof that written language creates its own grammatical needs over time.
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