How to calculate the rate to pay a recruiting agency for new students? When a university allows agencies in other countries (perhaps in the same country?) to recruit students for them, as I understand it, the university will pay the agency some fee for each student admitted. How is the compensation calculated?

Are there universal standards? Perhaps by country? If no standards exist, how would one even start the negotiations with the agencies?

Related to this question is how the agencies protect themselves while the university also protects itself. What if a student comes to the university and forgets to say "ABC Ltd sent me" but later ABC finds out that their student did start and now ABC wants paid.

I'm specifically curious about UK universities and undergraduate students entering universities focusing on business/economics but any information about other geographical areas / subjects could also be helpful.
This is the only reference to their compensation I could find. In the UK case, average compensation/student in 2013 was about £4,300, which is about 50% of maximum annual tuition UK universities can charge to EU students (a limit that apparently does not apply to internationals) - all data as presented in the linked article. As other comments mentioned, and they seem ubiquitous, I'd request a sample of their standard contracts to get a better idea. This site seems to have decent traffic. Like all related links I could find, it rings all kind of alarm bells, but maybe you find it of use. For the U.S. case, someone put together some legal advice which you can download (as all this strikes me as fishy, I didn't dare to, so unsure if it's useful). I would definitely talk to your own school's legal counsel before taking any steps.