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Ah, another flamewar topic!
Well that's not my intention. I really want to know what's going on here.
Why would the edges of the plates start spraying charges into the air? As
the plates are separated, the capacitance drops to a low value. The
charge on the plates doesn't change, and by V = Q/C it causes the
potential difference to go through the roof.
Assuming we have an ideal parallel-plate capacitor, the potential
difference goes through the roof as you separate the plates, but the
electric field does not.