To surround a place or crowd around someone, pressing in from all sides.
From Old French 'aseger' (a- 'to' + seger 'to seat,' related to 'siege'). Originally a military term meaning to lay siege to a fortified place, later generalized to mean surrounding or crowding around.
This word is basically 'siege' with a prefix, and both come from the military idea of 'sitting' around a fortress—which is why reporters 'assiege' a celebrity and protesters 'assiege' a building, using the same siege mentality in modern contexts!
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