'centrally-assessed' is a modern English compound formed from the adverb 'centrally' and the past participle 'assessed' (from the verb 'assess'). 'Centrally' comes from 'central' + '-ly'; 'central' ultimately from Latin/Greek roots meaning 'center'. 'Assessed' is the past participle of 'assess', originally from Latin.

'centrally' developed from adjective 'central' (from Medieval Latin 'centralis' < Latin 'centrum' < Greek 'kentron' meaning 'center'). 'assess' entered English from Old French/Medieval Latin forms (via Latin 'assessare' or related formations) and gave the past participle 'assessed'. The compound 'centrally-assessed' is a modern formation in English combining these elements to describe evaluation by a central authority.

Individually, 'central' originally referred to the physical 'center' and 'assess' originally had legal/administrative senses (e.g., to sit near or to determine a value). Over time these combined elements produced the modern sense 'evaluated by a central authority' rather than a literal spatial meaning.