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Was Tarkin doctrine that effective against systems out of the border of the empire?

"The more you tighten your grip Tarkin, the more star systems will slip through your fingers"

No. But also yes...

The Tarkin Doctrine focussed too much on heavy firepower, huge capital ships. The majority of the fringe systems didn't earn the attention of a full fledged Star Destroyer.

Usually the answe is to send numerous small patrol ships. Problem with that is the imperial navy wasn't meant for war but to intimidate local systems. Anything short of a Star Destroyer didn't really do it.

The important thing to note though is that once a system deserved the attention of the Imperial Fleet, then yes, it was effective.

I mean it has prooven to be effective in more mercifull hand.
After his death some weapon like the galaxy gun make the empire enar unstopable.. Many system just surredner...