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#11
Uninstalling the Product key is only local, to remove a Product Key being moved elsewhere so that when it connects to the internet it won't be rudely deactivated because the Key has a new hardware signature. However the installation which Product Key has been uninstalled will immediately be flagged as non-geniune unless rearmed temporarily.
To deactivate in MS activation servers the current hardware signature tied to the key needs to be overwritten with a new hardware signature which is done during activation.
This is the reason if there is an existing hardware signature tied to that Product Key the robocall asks how many computers the Product key is installed upon, to which the only acceptable answer is one. This gives the go-ahead to overwrite the previous hardware signature with the new one, and if the previous installation connects to the internet it will be deactivated.
This has been pieced together from years of experience, and comments in our Activation forum here - especially by Bill2 who is especially expert on this.