How does Luden's Echo work with Karthus' ult?

The way ludens works, as I understand it, is that it applies the bonus damage on up to 5 targets. In otherwords, if you hit a ryze q, the initial target takes the 100+ bonus dmg as well as up to 4 targets near him.

If you hit a nami bubble on two people, they both take the 100+ bonus damage as well as up to 3 nearby targets.

Every person Karthus R hits takes the 100+ bonus damage, but there is no damage splashing off to nearby targets. (I have no idea how this works if someone on the enemy team is dead though)

I know there was a thread a while back about ludens not working with karthus ult and it was resolved that it actualy was working but only as bonus damage and no visible proc. Somehow the question never came up about if an enemy was dead.

Yes it does. It will not proc on toggle abilities however

But does it proc on every instance? for example, If I use my ultimate on the enemy team with luden's proc will it bounce off every person? If 4 of them were together would the splash hit all 4 of them 4 times? Or would it only proc on one target? How does it choose that target?

AwesomeChad you didn't answer the real question, WHEN does it proc? and on who?