Most central; closest to the exact middle or center point of something.
From 'centre' + '-most' (superlative suffix meaning most, as in 'topmost' or 'foremost'). An archaic or rare English formation following Old English superlative patterns.
This is a delightfully redundant word—'centre' already means middle, so 'centremost' is like saying 'the most middle-est part,' which shows how English speakers sometimes pile superlatives on top of each other for emphasis!
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