What is "Auto" Mode?
Martian Universities have two modes, "Auto" and manually selected speciality.
If you set the mode to a specialty then the University will only graduate that type of specialist.
"Auto" mode is not so auto. If there is a demand for any specialist in your colony the University shows that in the list of specialists.
Demand means you have open specialist positions but not enough trained colonists in that specialty able to work.
It will go down that list and graduate the most needed specialist (the specialty with the most demand numbers on it) first, see the notes below.
Then when all the demand is met and all the specialties are zero it randomly selects a specialty from all the specialties and assigns that to the graduating colonist.
It takes nothing else into consideration.
So I developed this mod. See Features.

How the University Knows you need Specialists
Its a simple formula but not what most people think happens.
A colonist does not go through University with a particular specialization being trained.
Instead a colonist gets generic training points while in University (nothing important - similar to Liberal Arts degree). See Discussion on Graduation Time.
Then upon graduation a specialty is assigned to the graduate.
Just before the colonist gets a specialization the University asks the game AI what specialties are most needed-what is the demand.
The game goes to each building that can employ a specialty.
It counts the number of maximum work slots that are not disabled (shift or slot turned off = disabled).
A list of all specialties and maximum number of specialists the Colony can employ is returned.
The University then asks the game how many of each specialist exists is in the colony, excluding those that cannot work (typically children and seniors unless you have seniors can work tech) .
The difference between maximum can employ and current working specialists is the number of needed specialists per specialty-the demand.
I bet you didnt think this is how those numbers in the University get populated.
The specialty assigned to the graduate is always the one that is in demand the most.

What happens when you need the same amount of specialists for multiple specialties(demand for two or more specialties is equal)?
The first specialty needing workers is selected which lowers that specialty demand by one. Then it continues with the next highest demand.

What happens when one specialty is higher in demand than another specialty? The university will continue to graduate that one specialty until it is lower than the next higher specialty demand.

What happens when I dont need any specialists and demand is zero across the board?
A random specialty is selected from the list of all specialties.

Will all my colonists eventually get trained and specialized?
Yes, eventually everyone will get an education if the Uni is always open. You will have zero untrained colonists if you let the Uni continue to operate.