'unbranchedly' originates from English, built from the prefix 'un-' (meaning 'not'), the adjective 'branched' (past participle/adjectival form of 'branch'), and the adverbial suffix '-ly'.

'branch' comes into Middle English as 'branche' from Old French 'branche' (from Late Latin/medieval Latin 'branca' meaning 'paw' or 'claw'); it developed the sense 'limb of a tree' in English. 'branched' is the past-participial/adjectival form, and the modern adverb 'unbranchedly' is formed by adding 'un-' and '-ly' to that adjective.

Originally related to 'paw' or 'claw' in earlier Romance/Germanic sources, 'branch' came to mean a limb or offshoot (e.g., of a tree); 'unbranchedly' has the straightforward modern meaning 'in a manner that lacks branches.'