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Like he did with Palpatine? You know, the guy who was more powerful to begin with? Sorry, but your logic is becoming circular. Vader followed Tarkin's orders, and reported to him several times throughout ANH. You are more than welcome to read more into the all you want, but Vader is clearly under the command of a mere human.
You haven't proved that Vader doesn't see Tarkin as any more than a subordintate. So, acording to your logic, if in between Ep III and the end of ANH, (hypothetically) the Emperor were to die of a heart attack, you're thinking is that Tarkin would become Emperor and Vader would still sit there all the while thinking: yes I could force choke this dude, and yes I an the 'chosen one, but I better not since Palps liked him? Correct?