How is the interrail ticket price is distributed to European railway companies?

That is just the reason why this trip-report is there-in the past-or still on old-style paper passes you have to write down-and one was asked (in the start even enticed to with a reward-even some money back if done at station-where in that time all passes were sold) to return this to the main office. They would then -roughly- count what trips were spent in what countries-then a complicated formula (IT fares are much lower as SE fares-let alone CH or UK) was done and in the end the revenue (less cost) was distributed to the railways. Tipically most passes were sold in the north (yes, Scandinavia always won) and used in the south (the most populair route for long was Roma-Firenze in IT)-so money was also transferred. It was a temporary job for working students to do that. But as more and more people did not return the pass-keep it as souvenir-a new trick had to be invented. Then they would return pass after this if so required.

In that time there were only state-railways-the very few others simply did not participate. But now many countries have contracted out the services and f.e. in DE=Germany there are some 50 different companies.

So the main reason to go mobile was to make this process much more technological. And thats why the idea still hangs on that one should carefully and exactly write down all trips-as on 1 line 3 or 4 companies may run.

This is also explained in a few wikipedia pages, but I dk in what languages.

There is always a “National Group” above these railcompanies 

In Case of the UK it was called ATOC now RDG (RailDelivery Group) 

RDG get´s the money from Eurail :)