I didn't really mean to do it.  Honest.

I triggered the Benevolent Ideology perk, Enticing.  All planets and starbases in my territory flipped to me.  I was looking to get a few minor faction planets I had planted Culture starbases by in preparation for the flip.  I had a total of 5 administrators left after doing all tech increases.  It was tight.  I expected to get some of those administrators back when I didn't need the culture bases anymore.

I had forgotten about the AI's annoying habit of littering my space with resource mines.  I wasn't using those resources, they seemed to think, so why not?  And every one of those mining bases flipped to me.  I now have a list of about 40 resource mines and totally ridiculous amounts of resources.  I destroyed a culture base just to test, and now I have 6 administrators.

There is a hover tip that says I am using 96/102 administrators.  I am on an Immense map.  I am pretty sure that is a higher max than I had before.  My guess is you get the administrators along with the starbases.  When I decommission two of the newly acquired starbases, my available administrator count goes up to 8 and the hover tip says 94/102.

Yay for being Benevolent!