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Of course the accelerator pump on a carburetor is mechanical, and yes, it squirts a small amount of fuel into the intake when you initially step on the gas. You can customize the accelerator pumps fuel curve (amount of fuel and length of time to deliver) by changing the pump cam, pump lever, pump lever pivot point, fuel discharge nozzles, etc. Fortunately, the TPS replaced all this.
On an electronic fuel injection system, the computer uses the voltage from the TPS to calculate all the things you listed. But then what does it do with the information? Usually nothing, it almost always ignores it! However, if the computer decides the TPS voltage means you just stepped on the gas it briefly overrides the normal fuel curve and adds more fuel, by temporarily changing the injector pulse, so the engine will not bog. That is why I said in the original post, the TPS is the modern electronic equivalent of an accelerator pump.
The only other TPS function is to indicate a closed throttle or WOT condition. In either case, the computer then reverts to preset fuel curves until the TPS signal changes.
Your post did not list an alternative purpose for the TPS. If I am wrong and it does not replace the accelerator pump, what does the computer do with the signal? Why does the system need a TPS?
Umm, kinda--

however the signal is used for many things-including the transmission.