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big corporations only have the power they do (and only get big) because of the influence of federal government.

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So it is your unequivocal claim that big corporations (or an analogue to corporation) would not exist under AC? Do you want to share with us how you know that?

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A "corporation" as we know it is a *creation* of the state. The *state* grants limited liability to the owners.

So yes, without a state, there will be no "corporations" with state-provided liability shields. Do you want to share with us how you think the situation could be otherwise?