'unbranchedness' is formed in modern English from the prefix 'un-' (a negating prefix), the adjective 'branched' (from 'branch'), and the noun-forming suffix '-ness'.

'branch' entered English from Old French 'branche' (Middle English 'branche'), ultimately from a Germanic source (compare Old High German 'branca' for 'burning stick' or 'twig'); the adjective 'branched' developed by adding '-ed' to 'branch', and '-ness' was later added to form the abstract noun 'unbranchedness'.

Originally 'branch' referred to a limb or twig; over time it retained the basic meaning of a subdivision or offshoot and has combined with productive English prefixes and suffixes to create terms like 'unbranchedness' meaning 'the condition of not having branches'.