Jungle
Drop W across the way out, not behind the fight, then keep the trapped target on your side of the wall with isolated Qs and an E toggle that stays on only for contact; that wall-line plus mana discipline is a huge part of real Karthus damage
Karthus is best when the map has already started to break: full clear, buy level 6, and arrive for the skirmish that is already happening, because he is much better at collecting the second half of a fight with passive and R than at inventing a clean early gank from nothing
Deaths can be profitable on Karthus if the enemy is already stuck finishing the play inside your wall, aura, passive, and ult, and the recent data supports that he tolerates messy high-death wins better than similar AP junglers even though 9+ deaths usually means you died before you made them pay
Use R when it collects a fight that already happened, not when it is merely available. The clean casts usually come in three spots: after a skirmish where two or three people are already trying to leave on low HP, during your passive when your positioning cost is already paid, or right before the enemy can reset a dive or objective and walk out clean. If pressing R now only adds chip and gives up your threat for the next 2 minutes, wait. If it turns damage you already created with W, E, passive, or a cross-map scrap into guaranteed deaths or forced recalls, cast it immediately.
Upon dying, Karthus enters a spirit form that allows him to continue casting spells.
Karthus unleashes a delayed blast at a location, dealing damage to nearby enemies. Deals increased damage to isolated enemies.
Karthus creates a passable screen of leeching energy. Any enemy units that walk through the screen have their Move Speed and Magic Resist reduced for a period.
Karthus passively steals energy from his victims, gaining Mana on each kill. Alternatively, Karthus can surround himself in the souls of his prey, dealing damage to nearby enemies, but quickly draining his own Mana.
After channeling for 3 seconds, Karthus deals damage to all enemy champions.
