It has been bugging me that I couldn't find the following information on the internet, so I decided to acquire the info when I found out about the CHARGER Doctor that I found on e-Bay. I tested using a USB 2.0 hub that was connected to USB OTG to the smartphone and continued plugging more stuff in until the current peaked out. I found that charging a smartphone put a 0.45A load on the Note II and Note III, so I added more stuff until the measured current stopped increasing.
Galaxy Note II smartphone provides 500mA of current on the USB OTG connection.
Galaxy Note III smartphone provides 900mA of current on the USB OTG connection. Also, I confirmed that the stock music player played at 96k per the indicator on the Music Streamer II+ when playing 96k content, so UARP wouldn't be required for high-resolution playback.
HTC One smartphone provides 300mA of current on the USB OTG connection.
For some reason, I tried two different USB 3.0 OTG cables, and neither one initiated a USB 3.0 connection with the Western Digital My Passport external hard drive. The drive copied at USB 2.0 speeds as confirmed by FX File Manager when performing a file transfer.