Yes you can!

You can potentially turn off all other education buildings after building a university - all education buildings convert kids into students and subsequently enrol that student, however each education building provides a different level of education and influences the tech level of your industry.

Thus, I present to you Arcadia!

Here is how I came to my conclusion - I was previously of the opinion that 'students' and 'kids' were separate agents and being unable to find anything solid to confirm it either way, so I figured it was time for science!

If you are not reaching the maximum number of students enrolled, it will like be down to one of the following reasons;

• Not enough capacity
• Not enough coverage
• Traffic

Universities provide the highest level of education and the biggest boost to your industry (to tech level 3), but relies on your city's mass transit system and road network to allow your students to get to it. School buses will not drop students off at university. A university also allows you to research projects to create great works for your region and provide upgrades for your buildings.

A community college provides many of the educational benefits of a university and is smaller in size, but doesn't provide the same amount of improvement to your industry (to tech level 2 only).

If you have a university in your city, you should consider shutting down your community college, provided your road network and mass transit can handle it your university will have no problems teaching the students from your college.

Grade schools and high schools are basically the same building but with different capacities. Each provides its own transit system that can pick up students but provides a lower level of education than a university or community college.

You do not need a grade school or a high school, but it's worthwhile having at least one for the benefits that they provide as these schools will pick up the kids in your city to keep them off the streets, reduce crime, pollution, trash and energy consumption while providing a bonus to the amount your sims recycle.

As for getting the maximum tech level and maximum education level just with a university? It's not impossible. In many of my screenshots above you can see that I'm at tech level 3 with just a university, but the overall education level hovered at around 3 out of 5. I didn't get an education level higher than 4 during any of my testing with universities so this leads me to believe that either not enough time was given to allow the education level to rise to maximum (the oldest city I used during testing had only got to year 3) or that it isn't possible to get the maximum education level with just a university.

One of the main challenges I faced while trying to build a comprehensive education system that enrolled all students was transport, sending out fleets of buses would gridlock my road network during school hours. One tip I have for this as a result of my testing is that all a school bus will drop off students at another school of the same type, regardless of whether that bus originated from that school.

A few things I noticed while testing

I noticed that the value for the number of students being taught on the university overview is another number that doesn't tally up with the education overview;

This city has never had a grade school, high school, public library or community college - the only source of education has been via the University.

A university is also able to teach in excess of the maximum number of students that can be in class at once;

I noticed that during the initial growth of the city, the number of sims enrolled would lag behind the spurts in growth in that large portions of the population were not enrolled;

A few months later and you start to see your overall education level rise. As the population increase begins to plateau the number of enrolled students catches up to the total number of students available, although I still haven't seen the number of enrolled students at 100% at this point;

By this point, I am noticing that I'm getting a fair quantity of "Too many injuries - moving!" - which is usually a sign of low education, however my overall education level is still increasing, and my industry tech level has already reached 3.

In addition, I am still seeing a specific group of sims that are not enrolled into my education system. In the following two screenshots, you will see Kids represented by purple bars (which is actually shown on the data layer as not enrolled) and Students represented by green bars (which also means enrolled);

In all instances, the purple bars identify themselves as X Kids, while the green bars identify themselves as X Students;

When the university is in use, it is populated by students. With this in mind, I plopped down a high school - the next morning the education data layer showed no instances of people not being enrolled while the total number of students enrolled wasn't at 100%;

In the above screenshot, you can see a new set of 'blue' bars - these bars represent kids/students waiting at school bus stops. In this instance, all of the kids have relocated to waiting at the bus stops for their high school buses (note that universities do not have a dedicated transit service).

Shortly after placing the High School my city went through a sudden population growth phase which increased the number of kids in the city. With all of the additional kids in the city I was able to see a pattern. Outside of school hours my education data layer would look like this;

Then, once the school buses had started picking the kids up for school, which is shortly after the school opens at 6am, my city's education data layer would look like this;

During this, my number of students enrolled did not noticeably fluctuate, and neither did the number of students being taught at my university, however the number of kids in the city had reduced and were arriving at the high school.

To mitigate the traffic problems I was having, I made a new city to test with. In this city I built a road network that didn't suffer from the same traffic problems - I found that my overall enrolment reached 100% quite quickly. Even at 100%, looking at the education data layer showed un-enrolled sims;

Like before, these were all kids, and adding a high school to the city would get them off the streets and show no un-enrolled sims on the education data layer.

For an additional test, I built a city that only had a high school to try and work out exactly what effects a high school has;

Again the purple bars when you hover over them show up as kids in all instances. After 6am the fleet of school buses set off, and pick up all of the kids from the various bus stops, and the education data layer shows this;

In every instance of a bus picking up a kid form their home, that kid turned into a student upon arrival at the high school.

For further testing I destroyed the high school and left the city until the number of students enrolled had reduced back to zero and then built a grade school in the same location that the high school previously resided;

However after the fleet of school buses went out at 6am, the results were pretty conclusive in that enrolment increased to the point where the grade school was full;

The grade school was already fully upgraded so it was not possible to increase the capacity further so I added enough additional grade schools to cater for the maximum number of potential students that could enrol and waited until the next day. While this still didn't result in reaching the maximum possible number of students (due to a localised capacity issue) I am confident it would be possible to get 100% of all students enrolled using just grade schools;

In order to do so though, required a new city - one of the main problems I've faced trying to get 100% enrolment in large cities is that school buses clog up your road network quite easily if you're trying to fetch all your students from one centralised location. In this city I placed four grade schools, one in each corner;

Yes and no - universities rely on your city's mass transit system and road network to allow your students to get to it. School buses will not drop students off at a university, therefore only students that can arrive using mass transit or a car will go to a university.

Grade schools and high schools on the other hand provide their own transport, it still relies on your road network but is separate from your mass transit. These schools will pick up students from school bus stops, and students will wait for the buses at the school stops provided that the stop is within walking distance (highlighted by the dots along the road when you place the stop, or detailed on the education overview).

One of the main challenges I faced while trying to build a comprehensive education system that enrolled all students was transport, sending out fleets of buses would gridlock my road network during school hours - if your students can't get to a school they will unenroll.

I have written up a comprehensive answer here