The goal of this build is to turn Kog'maw into an independent killing machine that can't easily be focused down.

Why worry about defense? Kog'maw is not good at escaping trouble when it finds him, so he needs to be able to go toe-to-toe for a brief time with enemy champions. Otherwise, he tends to get focused and dropped early in the fight and a dead carry does no damage.

Why on-hit (meaning high attack speed and items that do damage on hit) instead of attack damage (AD) or ability power (AP)? AD and AP are both viable ways to build Kog'maw, but I find AP Kog'maw is too easy to dodge and AD Kog'maw is too easy to counter. An on-hit build synergizes perfectly with his Q and W, provides good defensive benefits built into the items, and is really hard to counter with defense since both physical and magical damage is incoming in high quantities.

Combined offensive output and toughness make enemies frequently underestimate this build. Kog'maw is supposed to be squishy but assassins are in for a surprise when they leap in and you tear them apart after surviving their burst. You can't escape them anyway as Kog'maw, might as well beat them handily.

My rune choices here are simple. More attack speed from marks, as this is an attack speed heavy build. More HP from seals because hit points are helpful against all opponents and it works towards building him some toughness. Magic resist glyphs round out the build since the only other source of magic resist here is Wit's End.

I frequently see people buying mana regen for on-hit Kog'maw from glyphs but Dominion gives more than enough mana regen passively to fuel your needs. As long as you fire your Living Artillery sparingly (once every 5 seconds with a few runs of 2-3 in a row now and then) mana will not be a problem. Living Artillery is fairly weak anyway on this build and not worth spamming unless you're in attack range fighting in which case the fight won't go on that long.

The primary tree is offense (for a carry? who'd have thought?!) Avoid Deadliness and Lethality because they don't synergize well with your build. Take more Brute Force than Mental Force because the former synergizes better with all the attack speed. Both Weapon Expertise and Arcane Knowledge are helpful since you do both kinds of damage. Finally, with 3 points to spend in the late offense tree the choices come down to Vampirism vs. Sunder . Both are reasonably helpful, but I prefer Vampirism for a little more sustainability and because life steal works for on-hit effects.

The extra HP from the defense mastery works with the rest of the bonus HP sources here to give Kog'maw more staying power, even early game. They help balance out the lack of a prospector's item as well.

The item build and progression is designed for attack speed, on-hit effects, and just enough durability to be a bruiser in your own right. One advantage of an on-hit build is that it tends to be fairly inexpensive; all together this build cost is 12,830 which is very achievable in most games, especially compared to the AD builds which tend to run above the 14,000 mark even with leaving a prospector's item in. However, buy order and some items are going to vary widely between matches depending on who you're fighting and how they're doing. This does mean that I'll sometimes finish the game with 4,000 or more in the bank (see screenshot section below), but that means I've been seriously dominating, so that's OK.

Boots are best either as Berserker's Greaves, Mobility Boots, or, in the case of heavy enemy crowd control, Mercury's Treads. I prefer Berserker's Greaves for maximum dueling potential, but Mobility Boots are going to be better for getting to crisis areas quickly. If you find yourself moving from place to place more as you play, go for the mobility. If you find you tend to push and defend in one area, the attack speed is better. It comes down to play style. Once you get good at reading enemy intentions and the flow of Dominion you will know more often where you're going to be needed and can anticipate more often rather than react, reducing the need for the extra mobility.

My first on-hit item is always Wit's End. It's cheap, it does the highest flat damage of any item so is the best early-game on-hit item, and it boosts magic resist for early game survivability. After boots I can afford the Null-Magic Mantle component and a health potion at the start of the game. However, against a team without much AP you can forego the Null-Magic Mantle on your first trip out and with luck earn enough to buy a Recurve Bow on your first trip back. Otherwise, you're probably not buying anything your first trip home.

Buy order after that is fairly flexible and depends on the situation. If they've got a lot of AD, Chain Vest is going to be a great early buy, with Thornmail being something you want by mid-game at the latest. If they've got stealth characters, Lightbringer moves up to your next full item ahead of Kitae's Bloodrazor. Quicksilver Sash may become a must-buy against certain champions with heavy CC like Morgana or Malzahar, taking the place of The Lightbringer or Thornmail (but moved to sooner in the buy order.)

Against a reasonably balanced team after Wit's End I like to next grab a Ruby Crystal, a Recurve Bow, and a Chain Vest. What order I do so depends on how much money I have and how I'm doing. If I can afford it the Recurve Bow is usually first if my survivability seems OK or I'm not receiving much pressure from the enemy team. If I'm having trouble with AD champions or survivability in general I'm going to grab the Chain Vest or Ruby Crystal first.

Next I build the Phage to help with chasing, and since my attack speed is pretty good at this point (+130% or so) the passive procs pretty regularly which helps me out every now and then to catch someone.

Next comes Kitae's Bloodrazor, which is pretty much the signature item of this build. with Bio-Arcane Barrage you're doing 8.5% of their max HP in magic damage with an obscenely fast attack speed. This lets you even kill high-HP tanks or characters like Olaf really quickly, something that AD builds cannot do nearly as well.

Now that the murder potential has gone up, it's time to focus on toughness and utility. Frozen Mallet does both and makes it fairly impossible to escape you thanks to your range from Bio-Arcane Barrage, Living Artillery, and the slow component. Even Flash doesn't them far enough away oftentimes, especially combined with The Lightbringer.

If you haven't yet, buying Thornmail now is a pretty good idea if your enemy has at least 2 AD characters, or 1 AD character who is dominating. If their AD isn't giving you any trouble, save Thornmail for last. Why Thornmail? Because it's the most armor for the least money and shuts down AD carries most effectively for the price. If you have extra cash lying around at the end of the game, you may consider replacing the Thornmail with a Frozen Heart for a little extra mana, cooldown reduction, and group utility. AD carries should know better than to attack you solo by this point anyway. If they don't have any true AD at all, consider a Odyn's Veil or Maw of Malmortius instead. Also laugh, laugh at their team composition.

Finally, the last item is a tie for me between The Lightbringer and Ionic Spark. The The Lightbringer is better for chasing enemies through the jungle and countering stealth or teleportation. The Ionic Spark makes you a little tougher and does a little more offense. Here's some situations that clearly merit one over the other:
1) Enemies have stacked significantly more magic resist than armor = Take The Lightbringer
2) Enemy team has stealth characters like Shaco, Akali, or Wukong or teleporters like Kassadin= Take The Lightbringer
3) You're fighting a lot in the jungle = Take The Lightbringer
4) Enemies have stacked significantly more armor than magic resist = Take Ionic Spark
5) You're mostly fighting in lanes, doing a significant amount of minion slaughter, most fights involve many characters, or you're getting focused by melee characters fairly often = Take Ionic Spark

All things being equal, The Lightbringer is a little nicer for all-around utility while Ionic Spark is a little better for beating people outright in combat. I tend to hang out in lanes and defend points so Ionic Sparktends to be my pick, but it varies by circumstance. Killing a fleeing Kassadin or someone flashing over a wall with your Living Artillery thanks to the The Lightbringer passive feels like unlocking an achievement.

The best advice I ever got for Kog'maw's skill sequence was to level Caustic Spittle first vs. melee opponents and Bio-Arcane Barrage first vs. ranged opponents. So depending on your enemy team's comp you may want one or the other. I find the extra range and damage from Bio-Arcane Barrage to be most helpful against a balanced opposing team.

Ghost is pretty much a must-have for all champions in Dominion, possibly excepting someone who does nothing but bottom lane the whole game. Getting where you need to be in a clinch is vital. However, you don't always need to be rushing somewhere, hence the boots discussion above.

For the other slot Exhaust is my favorite, though Surge is also excellent. I tend to go for Exhaust because the snare component helps nail some early game kills and it helps when you're finishing off an opponent if you can exhaust the newcomer and then deal with them after you've killed the first opponent. Surge is nice because Kog'maw frequently gets exhausted and Surge is a good counter to that as well as a decent buff that lasts much longer than Exhaust. Late game, Surge is not very noticeable though in terms of increased damage output.

Another good Dominion pick is Garrison, though it's not as useful for Kog'maw since you can be effective from outside turret range. Mostly I like it for teamfights to keep my meatshield alive (whoever ran in and has the turret's attention as well as the enemy champions'.) The longer my meatshield lives, the more I get to dps freely, which makes for a very happy Kog'maw.

Finally, a few tips on playing Kog'maw in Dominion:

Use Living Artillery from the bushes above or below the Windmill (center point) to harass enemies and prevent captures there. Elsewhere, just use your range to prevent enemies from capturing points even if you're at low health because it will be extremely hard to find you and chase you since the shots can come from a great many places in the center jungle.

Use Living Artillery to check bushes for ambushes. It's cheap and reveals enemies, there's no point in not doing it if you suspect an ambush. If you know an enemy is in a bush, even better. You can flush them out or make them targetable at range.

Only spam Living Artillery when you're in a fight. Harassing at long range by using it every second isn't going to do much damage and will run you out of mana you need to fuel your other abilities.

Use Icathian Surprise to delay point captures. Even if you can't get a kill, buying some time with your death is worthwhile.

Thank you very much for reading. This is a rough version, and I hope to pretty it up. I wrote this because I disagreed with some of the choices made in some other Kog'maw dominion guides and wanted to address some Dominion playstyle/metagame issues.
Comments and criticism are very much appreciated.

Just putting some screenshots of this build working down here.

8/9/12 in a close game against a good team. They managed a pretty good comeback rally as we had trouble wherever I was not. I had to figure out which way they were pushing so I could be there to counter.