How does supply work through allied capitals?

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Krenn

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so, I've been playing the British Raj, and trying to pick paths that will allow me to fight in the Japan-China war as early as possible. preferably by joining the chinese faction.

But what's driving me crazy is that I THINK I'm sending more troops to within range of each chinese warlord's capital city than that city's supply depot can actually support...

But it also seems like no matter how many railroads I build between India's capital and the supply depots of Chinese Allies, it's very difficult to see how much benefit that's having, if any.

Can anyone provide some advice, there, in terms of how supply through allied capitals actually works? Does building a railroad between my capital hub and there capital hub actually do anything?

Sample map attached, trying to connect Delhi to Kunming.

1639677560592.png