There are some people that go different builds on Karthus I see stuff from Predator to even Phase rush so what runes puts out the most damage quickly and it effective early and late game? Also what builds should you go as Karthus? 
in ARAM
Predator Ultimate hunter (others don't really matter)
Secondary : Precision
Presence of mind - Last stand
Build : 
On SR there are a few different ways you can go, depending on your playstyle and who you're against.
Rune wise, I like to go Aery over comet - it's easier to proc and its definitely going to hit. While it only does a tiny amount of damage compared to comet, it has actually been the extra bit I've needed when ulting to secure the kill quite a few times.
Electrocute is an option, but I've always seen it as counterproductive to his playstyle. If you just farm up as Karth you'll be relevant, and electrocute forces you to trade with your opponent, opening up the option to die and fall behind - which is the last thing you want to be doing btw.
I forget what the other ones are called, but the rune that scales ad/ap with time is really good as well as the rune that reduces the CD of your ult if you get a kill with it.
Build wise, I rush catalyst almost 100% of the time. It provides a ton of sustain and just allows you to keep farming and staying in lane. Build it into RoA and than itemize as you see useful - my build usually looks something like: Catalyst > RoA > Sorc shoes > Void Staff > Morello > Deathcap > Zhonyas or liandrys or Rylias depending on whichever is most useful. The one exception would be rushing a seekers if youre against Zed/Talon and they have an early kill.
It's worth noting that in almost every single Karthus game I've played I've dealt the most damage. Karthus get absolutely out of control if you farm up and play smart.
Karthus is really similar to A Sol in how he benefits enormously from magic pen - you should probably always build sorc shoes, morellos, and DEFINITELY void staff regardless. When you're 6 items your ult can easily deal over 1k damage by itself.
Playstyle you should always be farming. Think 60 cs by 9 min. Don't even think about fighting until you've finished 1 or 2 items, because late mid game to late game you'll be hitting like a truck. It's also worth noting that in lane, karth has a distint advantage over melee champs because he can wipe out the line of caster minions in a second. I think it's 6 q's level one kills them all, at which you level up your w and start getting mana back from kills.
From playing him a lot, I actually think he doesn't have that many matchups he gets steamrolled in. Some of his harder matchups are the intuitive ones, Zed, Ekko, Kat. I would pick Karth into almost any patchup except those. If they're good youre going to get smashed and theres a high chance they'll snowball out of control. However, in that case just pick Diana.
Aery is better than Comet because Aery can move back to you faster than you can reset the cooldown on Comet. All of Karthus's abilities are AOE / Multi-target or DOT, so you are only able to shave 10% per target of the remaining cooldown by landing an ability at best. It isn't easy, nor do you really want to hit multiple targets with his Q.
Champions like Ahri are better with Comet because her Charm, and each of the 3 Fox-Fire bolts count as a single-target ability and refunds 20% of her remaining cooldown on Comet if they damage champions.
I run a slew of different rune pages for Karthus depending on what I want to do.
While Aery is the standard for the Sorcery Tree, I will occasionally use Comet because I like the damage.
I run electrocute specifically when I'm dealing with an assassin that likes to get up close. I try to use it as my Anti-All in method. Exhaust is greatly recommended as well.
I like Predator when I'm wanting to add a deece amount of execute damage to my ult since Predator will proc on the Lowest Health Target for Large Scale AoE (Like say, a Karthus ult). I pair it with Precision secondary(Coup + Presence of Mind) when in lane, Sorcery in JG for the CDR.
Glacial Augment is a rune I don't use very often, but I think it would be good if you're going for a Support Karthus playstlye so you can run things like GLP and Spooky Ghosts.
I try to vary my builds as well, depending on Matchups and the like. If I know I need to scale, but I don't necessarily need to off tank, I'll go AAS. If I need powerful poke, I'll get Luden's. When I jungle, I'll go both Runic and GLP for the slows (If against an Assassin Jungler, this could let me go Red smite to reduce the burst and still have a slow option). Most builds afterward have me build Boots standard, Deathcap if nobody is building MR, Void if everyone IS building MR, Then the choice is if the enemy team is building Heals or Health. If Heals, go Morellonomicon, but if stacking health, go Liandry's.
