Does the rollover function simply move students from their current year to the next academic year? Can I mimic the rollover in manual steps. What would those steps be?
Yep. However, it doesn’t actually move them but rather copies their current enrollment to the next academic year.
Why mimicing this in manual steps if you can automatically rollover all your students? 
The rollover also deals with students who are leaving, and allows you to set up a combination of automated moves to new form groups with custom moves, so everything can be preset in advance. Roman asks a good question there…I am curious about the answers!
Check our the relevant docs for more detail: https://docs.gibbonedu.org/administrators/timetable/rollover/
Ross
I do not intend to do this manually. My asking about the steps was really just to let me understand what is (and is not) happening in the background when you click on that button. Thanks for your answers 
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Ah, I see! What is involved is updating gibbonSchoolYear to jump the Current flag up one sequenceNumber. After that there are new entries made in gibbonStudentEnrolment, and status changes in gibbonPerson (e.g. Expected to Full or Full to Left). Hope this helps! Ross