I think you can look it up with the editor on the country settings. Fully co-operative would be supply and HQ sharing. Cooperative only supply. Russia and Japan are non cooperative so the do not provide any supply to allies. China provides supply to the western allies,
I'm not sure about Chinese supply for the USSR, I would assume the do not provide supply to them. For minor countries it depends if they are surrenderd or liberated.
If they are the provide only supply for the country who owns them. If they have not surredered each city provides supply for the country who last entered it. So if Iran did not surrender some cities can provide supply for UK other for USSR.