Not Updated For Current Season
I will like to point out some things that most people dont take advantage of with karthus and that is 2 things zhonyas rin and ur ability to kill steal with ur ult.
in general i have found the better path to a good karthus is that of self sacrific i am usually the battle initator wheni jump on a team usuing my W. i then will use zohnya's ring and they will usually all just stay there now by the time ur done dyeing u should be able to take out 1 maybe 2 and leaving almost there intire party at 50% life or less leave team clean up plus ur ult a masterwork of carnage.
Now DO NOT use ur alt to steal enemies ur team is currrently engaging instead get the ones that get away(behind the tower that is) now note that at lvl 6 ur ult will do aprox 2 bars of health to those with no MR. So dont waste it.
also note that if u do build this build and sacrifice ur boots in the end u will have 1286 ap
hope this helps you out i am at a 75% win ratio with karthus and i have play aprox 50 or so games GLHF