'much-debated' is formed from 'much' and the past participle 'debated'. 'much' originates from Old English 'mycel' meaning 'great' or 'large', and 'debated' comes from the verb 'debate' (see below).

'debate' entered English via Old French (e.g. 'debatre'/'debatre') from Late Latin/French roots ultimately related to Latin 'battuere' (to beat). It became Middle English 'debaten' and later modern English 'debate'; the past participle yielded 'debated', which combined with 'much' to form the compound adjective 'much-debated'.

Originally the root idea (from Latin 'battuere') had senses of striking or fighting; over time this shifted in Romance and later English to a sense of arguing or disputing, and today 'much-debated' means 'widely discussed or controversial'.