I get the impression that the banker has some elaborate set up that deals with my and other region's food surplus. But having never been a banker I don't know if this is true.
Am I the only one who deals with my surplus, or is it possibly being carted out to feed the cities by the banker through some artificial function?
Very much depends on what system your realm uses. Some realms do indeed have centralized control by the Banker, some have control at the duchy level, and some have control left to the regionlords. Unless it's one of the half-dozen realms I know the food situation in, I can't tell you anything beyond that, but a quick letter to the Banker and/or your Duke and/or your realm should clear that up.
