[absolootezer0]

you're right on the cig part, not the derogatory. In British English, the word "fag" was used (as a verb and a noun) to refer to a kind of apprenticeship practiced within public schools. Younger boys within the school "fagged" for the older boys by cooking breakfasts, cleaning sports kit (equipment) or other menial tasks. The term fag in this sense derived from the sense "flagging in energy due to having performed strenuous menial labour," as in "I'm all fagged out." Violence, bullying and sexual abuse were sometimes associated with fagging.

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OK. Thanks.