They have only outlined it in detail for WoW, but with Blizzard most of their policies are the same across all games.
Here is the policy
Multiboxing, or playing multiple World of Warcraft accounts at once, is not a violation of our End User License Agreement. Please note, however, that use of all software or hardware mechanisms used to mirror commands to multiple World of Warcraft accounts at the same time, or to automate or streamline multiboxing in any way may result in account penalties.
And here is further clarification.
I can confirm they DO ban in WoW now for ANY software or hardware facilitation of multiboxing. We have seen posts on the CS forums of people complaining about it.
They mean it when they say the terms “hardware” and “streamline”. Note that is not just software automation.
Anyone doing anything except totally manual multiboxing is doing so at their own risk.