> I am pretty sure Chinese citizens are allowed to [...] go to university if they score well enough on the public tests. Just like in Europe.

China implements a comprehensive system of geographic affirmative action to prevent universities from being taken over by southerners. A school participating in this system will publish a plan stating how many students it will enroll on a province-by-province basis. (It's also divided by whether the students will major in science or humanities.)

Once the tests are scored, the students in a particular province are assigned in top-down order of score to the school of their choice, as long as that school's quota for accepting students from that province is not yet full. If your school of choice has filled its quota, technically you can have listed a second-choice school, but this is widely viewed as a disaster for the student. You need to get in to your first-choice school, or take a year off and try again next year.

What's happening in admissions cells for other provinces at the school you apply to is not relevant to you. You can outscore 90% of students who get admitted that way and it won't matter.

And this is not an especially unlikely scenario, because Chinese policy is that schools have much larger quotas for local students than otherwise. I think you need to score at about the 1 in 60 level, top 1.66%, to get into a top Shanghai university from Shanghai; you need to do a lot better than that to get in from outside Shanghai.

Sanity checking that, the admission table for Fudan University in 2018 is here: https://ao.fudan.edu.cn/a7/19/c36333a435993/page.htm . This contains some annotations that I don't understand, but let's say you want to be admitted as a math major. The score threshold if you're coming from Shanghai appears to be 586 ("选考科目999"?); 586 on the Shanghai 2017 gaokao is top 1.1%, or in perfect detail the top 473 people out of 43,103 who took the test. ( https://news.koolearn.com/20170623/1127786.html )

The score threshold if you're coming from Fujian appears to be 680 on the science test. A 680 on the 2017 science test in Fujian means you were one of the top 72 scorers out of 86,368 people who took the test, or the top 0.00083%. ( https://max.book118.com/html/2021/0817/8104004033003135.shtm )

That admissions table for Fudan is divided into two categories, 提前批 ("advance admission"?) and 本一批 ("freshman admission"??). I'm not sure what they mean; I used the 本一批 numbers, which are stricter.

Relevant here, I knew someone who attended a high school affiliated with Fudan (a lot of Chinese universities have these), and she informed me that before taking the gaokao, she had an interview with someone at Fudan, and their approval of her meant that she needed a lower score for admission to Fudan than would otherwise have been necessary. I suspect that this may be related to the difference between "advance admission" and "freshman admission".

(There is also affirmative action given for non-geographic reasons. Sometimes they combine in interesting ways. A friend of mine who was admitted to 上海财经大学 benefited from a program for minorities. She was a Mongol, and would have been given a direct bonus to her gaokao score for that reason, but this program additionally involved (1) attending a special high school in Beijing, and (2) counting as a resident of Beijing, and therefore also benefiting from the geographic scheme, for admissions purposes.)