I have seen 0.41A reported by a USB volt/ammeter when a phone was connected to a controller with a 51% charge. From memory it was at slightly over 5V.
I wouldn't go experimenting to find the upper limit, it might be an expensive experiment.
I've not done any official testing with a device to measure the output but I tried a number of devices that support different fast charging or higher current charging and none of them showed the controller was outputting more than 500mA.