It runs separetely, but the gamepad will always turn itself on with the system no matter which controller you use. (likely due to the mic.) Also you can't use the pro controller to browse the internet, miiverse or the shopping channel so it feels slightly overpriced right now. I think the value of the pro controller will be better appreciated when Nintendo releases a Wii U specific virtual console, as someone in here noted earlier.

Has anyone tried connecting it to your PC yet? I used my wiimote for some games, and I wonder if I can use it. Is it mappable via Bluetooth? Or does it use Wi-Fi like the Gamepad?

My bluetooth dongle recognizes it as a game controller but I don't know the password. Eventually someone will develop a program for it.

Oh and I don't think the gamepad runs off Wifi. You'll notice your mii has an orange background when wifi is out.

It does run on WiFi... Different from your internet WiFi.

facepalm A WiFi connection and a wireless connection are two totally different things. You CAN'T have a WiFi connection different from the internet, because that's the whole purpose of WiFi, to connect you to the internet. Please research your topics before you post so you don't sound ignorant.

http://www.broadcom.com/press/release.php?id=s722281

Kindly take your own advice. The gamepad communicates with the wiiu using, among other means, a WiFi.

WiFi is by no means exclusive to connecting to the internet. WiFi is connecting between two devices. One such device is a router, which is one way to connect to the internet.

Touché. My bad

There are two separate WiFi radios in the Wii U. One running at 2.4Ghz and the other at 5Ghz. One is a point-to-point connection for the GamePad (5Ghz, hence the range limits) and the other is used to connect to your router. It's not that complicated. Both radios (think of them like two cables, one network and the other USB) can run at the same time.

The Pro Controller on the other hand uses bluetooth just like pretty much every other console controller out there. So it'll appear as a Bluetooth device if you try to connect it to your computer. Only a matter of time before someone gets it working as a PC controller assuming they haven't already.

source for claims about the wireless hardware:
Wii U: http://www.ifixit.com/Teardown/Nintendo+Wii+U+Teardown/11796/...
GamePad: http://www.ifixit.com/Teardown/Nintendo+Wii+U+Teardown/11796/...