Agree with the comments re using SD cards being the simpler option. Even on a 32GB SD card you start to struggle with navigating through all the folders etc. to find what you are after.
I have also been quite happy with the built in hard drive storage. Sure it is only 20GB, but it does mean that you can use things like the cover-flow interface and Audi voice recognition to navigate and find stuff. Downside is that it doesn't support custom playlists, but the upside is that it automatically organises everything for you, creates auto built-in playlists (based on track ratings etc. if you have maintained them in iTunes or similar) and most importantly (for me) it will let you play stuff using proper random across all your music. Unfortunately for SD card and USB, the random is confined to only the current folder for some stupid reason.
Anyway, in response to the original question regarding maximum capacity for a USB device, the MMI system will only read FAT or FAT32 filesystems. Therefore you will face a technical limit of 2TB per partition when using FAT32 (you wouldn't bother using FAT). The MMI system will also support a maximum of 4 partitions though so technically if one existed you could use an 8TB drive split into 4 partitions. The issue with all of this though is that the MMI track navigation system is simply not up to the task of dealing with huge volumes of media - in my opinion anyway. It is just too slow and cumbersome to navigate quickly between folders/files.
You also have these other limitations to consider (from pg. 20 of the MMI manual). From USB, the MMI system will handle a maximum of 5000 files per directory and a maximum of 1000 files per playlist. Audi also note that large numbers of files will affect performance of the system when reading the folder structures and file lists (although personally I haven't really noticed this yet).
Also the maximum bitrate for audio is 320kbit/sec, and although the system will play variable bitrate files (VBR), the time remaining will not calculate correctly... so if you have a choice i would suggest sticking with constant bitrate (CBR) encoding.
Embedded album artwork does show up if they are GIF, JPEG or PNG format and no larger than 800x800px in size.
Back to the SD/HDD conversation, I really would suggest using SD cards (as per other recommendations here) or the internal hard drive. The MMI cable interface is located in the most ridiculous location (almost smack-bang in the middle bottom of the centre console) and so by the time you have the cable plugged in and the hard drive in there you end up with no real useful room for anything else, and one thing the Q3 is already sorely lacking (IMO) is front cabin storage.
Cheers, Ivan.