The mid year mage update fixed many issues, but missed the biggest outlier.
Karthus is, at the moment, one tier higher in mid lane winrate than Urgot mid. He has no way to deal with people who buy boots, since it takes a simple sidestep to dodge a Karthus Q. He dies too fast in team fights and his passive form becomes an area opponents can ignore if they have a shred of mobility or defense, or if they're just passing through.
And his ultimate is one of the least impactful compared to its 5 minute cooldown, because you can negate it with something as simple as popping a potion biscuit beforehand. You have to get the exact calculations right, and be at least 100 damage over your opponents' HP (if they're squishy) to kill them. It doesn't even have a global quote to FEEL impactful.
Not to mention that Karthus is supposed to be THE late game battle mage, but lacks the proper tools to get there. His laning phase has been made painful since the W nerfs, making his W an over-glorified MR reduction zone. Karthus' bugs regarding his spontaneous and sporadic Q delays have been thoroughly ignored by Riot, and his E feels like it lacks any interactivity or use outside dealing an extra 100 damage to that Zed that dived you at level 6.
Karthus is one of the most suffering mages, and his win rate will now plummet since the changes to RoA hurt him as well. I love the new changes in the MYMU, don't get me wrong, but Karthus feels left out when he could've had the opportunity to shine.
Health stacking=
AP stacking=
Armor stacking=
if he builds it which gives AP off of maximum mana