Having overhauled many of these, I can tell you that centering the secondary likely won't center it in the corrector unless the secondary holder is, itself, dead center in the corrector.
It always seems to help to center the corrector plate in its cell, but note that there is a caveat to this: the primary itself may not be centered in the tube and the corrector needs to be centered on the primary, not the tube of the scope.
You only center the corrector if the primary is also centered. Otherwise, if the primary is off 1mm in a particular direction, offset the corrector in the same direction.
Then the alignment of the secondary: If the primary mirror's baffle does not have a front end (as seen through the back of the scope) that is concentric with the outline of the secondary (indicating the baffle, which is always perpendicular to the primary mirror) isn't pointed at the secondary mirror exactly), then the secondary must be off-center in the same direction the primary baffle indicates.
In the collimated scope, the corrector is off-center to match the primary, and the secondary is off-center to match the pointing of the primary baffle.
If you're extremely lucky, everything is centered in the tube as well.
When I worked on my old Meade 8", the only error was an off-center corrector, but everything else was perfectly aligned with the tube. And centering the corrector (and then re-centering the secondary) made a BIG difference (improvement) in the star images.
The final result was a tiny pinpoint with 1 or 2 diffraction rings around the stars.
But, from those I've seen, I was lucky. I guess they were making them a lot more slowly in 1993 than they are today.
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