At 3 items he gets pretty absurd damage and he gets even nuttier from there.
I play him top lane sometimes when I see a champ he can survive against (so something without enough dive * burst). Once you pick him into that situation he lamely farms top lane safely and scales into a monster, without having to worry about map presence mid lane or the range or assassins that like to be played there.
You must build him properly too.
is very essential as it gives your ghost massive control; it also enables you to land Q repeatedly. It is essential. Because you need Rylias you should just skip RoA imo because your build is
for mana and
. From there you can get traditional ap items or if you feeling frisky
for tank meltation and to force squishies into MR buys or recieve true damage from Karthus.
Playing him top lane is best IMO, while you need good positioning for most matchups and mana conservation particularly the first few levels he has kill pressure landing enough Q on melee and once you have rylias it's mega disgusting. I've consistently beaten amany pantheons and Fioras and such. Their gap closer isn't quite good enough. I would stay away from the Irelias and Wukongs though.
It's fun to hear that the enemy team flames their top laner while you exert map nukes and hyper scale.
Most people just aren't very good at Karthus because if you think about it he is like an immobile adc that has to skillshot every auto. However Rylias breaks Karthus. (no, just pressing R doesn't make you a good Karthus)
Oftentimes when Karthus top is on a team the whole team has such ridiculous damage his mid lane and adc can just one shot everyone. Karthus sorta performs the tank role by being a ridiculous threat that can't be stopped by killing and constantly emits slows.