I was feeling skeptical, so I decided to test this.
I still have trouble believing it, but Karthus's Q (when launched) appears to have a diameter almost as large as his attack range (450, assuming that it starts about where his character model begins)--i.e. a 400 unit diameter.
Wow...Karth Q is actually pretty big.
Some followup questions: What base sizes (in in-game units) are League characters' collision circles? What is the exact condition for hitting Karth Q or Brand W--does the unit's center have to be in the ability circle, or can their circles just overlap each other? (I believe it's that the distance between the champion's center and the ability's center is less than the sum of their radii (i.e. the collision circles overlap), but I just wanted to make sure).