Actually, the peak power supplied to a car at one of the stalls is 120 kW (roughly - I've actually seen slightly higher), but each Supercharger cabinet can put out 135 kW total to the two charging stalls it is connected to. So, with 8 stalls there are four Supercharger cabinets capable of 135 kW max each, or 540 kW max for the whole site.
(Correct me if I'm wrong, but that's my understanding from Cottonwood, who is never wrong.

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Well, I am not always correct...but I do try to get most facts right.
The total DC output of the four Supercharger Cabinets at 135 kW each, feeding 8 Charging Stalls is 540 kW. The AC power into these four Supercharger Cabinets at 90% efficiency is actually 600 kW from the transformer. Remember that is an absolute maximum with all cabinets running at maximum. An 8-Stall Supercharger like this is typically fed by a 500 kVA transformer because the utilities can size things like this allowing occasional operation at higher than rated capacity.
The Distribution Center has bus bars rated at 2,000 Amps. If run at the full 2,000 Amps at 480 Volts, 3-phase, that is 2,000*480*sqrt(3) or 1.66 megaWatts (1,663 kW). The limit is usually the wire from the transformer to the Distribution Center, not the bus bars in the Distribution Center. Below is a picture of the inside of a Distribution Center.
The Supercharging Cabinets are not rectifiers. See
Rectifier - Wikipedia; "Physically, rectifiers take a number of forms, including vacuum tube diodes, mercury-arc valves, copper and selenium oxide rectifiers, semiconductor diodes, silicon-controlled rectifiers and other silicon-based semiconductor switches." These sophisticated chargers present essentially a resistive load on the grid to offer a power factor of greater than 0.95 and draw current with a very low THD. This is about as friendly as a load can be to the grid.