I took it upon myself to create a viable Mordekaiser build for Dominion since a lot of people seem to struggle with him in that format. It's not perfect but it definitely works, here goes:
Quints: Flat Health
Marks: Magic Penetration
Seals: Armor per level
Glyphs: Magic Resist per level
Summoner spells: Ghost + Ignite
Link to Masteries: http://leaguecraft.com/masteries/1330440011300030103300000000000000000000000000000?
Role: Solo bot, pusher. Mordekaiser, as ever, has excelled at demolishing minion waves in a mere couple of seconds. (He can do well in other parts of the map, I just start bot because the build is fairly item dependent. This gives Morde a chance to farm up without dying too much early on)
Skill order: I think of this as standard, but perhaps there's some variation. At the start, I put 1 point into Q, 2 into E and 1 point into W at level 4. Max E first, then W, then Q with R whenever possible. Maximum shield generation and durability with scaling damage to late game.
My starting item if my teammates allow me to solo bottom is a Hextech Revolver and 5 health potions. From here it's fairly loose and adaptable but I generally start off going for a Hextech Gunblade and Sorcerer Shoes. Spell vamp is a very good choice for him but I feel as though during skirmishes on Dominion he takes a bit too much damage for the rate at which he gains/loses shield. Life steal supplements that and the Gunblade also gives us a gap-closer other than Ghost. Between those two items I consider my core, the build can go 2 ways.
Option 1, doing well: Tri-Force is my standby for increasing burst during a 1v1. Q damage is increased versus 1 target and Tri-Force adds just enough kick to have your opponents on their knees in short order. It also gives us extra damage for our life steal and more damage for our shield generation. As always, a great chasing item with the additional movement speed and slowing-proc.
After that killing is no longer an issue for Morde with his amazing longevity in combat. All he needs now are some key defensive items which should be chosen based on the largest threats to you. Force of Nature and Abyssal Scepter for casters who are fed, Thornmail and Sunfire cape are excellent choices for AD carries. You can always do a mix, go for Aegis of the Legion, Guardian, and Sunfire cape.
Option 2, if you're getting owned: Go straight away for defensive items. If you're getting beaten up by a tanky DPS or hard carry, go for Thornmail first, and then consider finishing your Gunblade. If you're still having problems, add in a Sunfire cape. Against a caster, Force of nature and Odin's Veil should allow you to hold your own until help arrives from other teammates. A good combination for a mixture is Odin's Veil + Thornmail. In a situation where you can't assault their bottom lane, your best alternative is to defend your own bottom point. The longer you can hold out, the better.
If you get to a point where you're surviving battles, it's time to grab a Tri-force and/or Rylai's Crystal Scepter. I find the Hybrid weapons are extremely useful once you obtain a Gunblade because they increase the effectiveness of both Life steal and Spell vamp.
General strategy: By pushing the bottom point and applying enough pressure they cannot just have one person bottom, you create a situation where your teammates are now fighting a 4v3 battle a good majority of the time. Even if you die in the attempt, capturing that top point, and recapturing your bottom point in the worst case scenario still puts you on top of the game. If you can maintain that cycle and force 2-3 enemy champs to defend bottom, map control for your team becomes a cake-walk.