A few things I need to explain that I do differently:

1. ITEMS

My item build suggestions are somewhat off-meta. They are designed to make you an absolute nightmare to go against. Yes, there are stronger AP items than Protobelt. However, try to imagine a Veigar with 1,000 AP who can Flash twice. Scary thought, no? And Mejai's more than makes up for it, if you win a team fight you will likely have at least an assist on everyone, probably some kills too, so you'll build the stacks back if you die in no time.

SUPPORT ITEM - This one is rather simple, Doran's Ring gives you more power to start and a bit more mana sustain, and you really don't need to bother wasting the gold on the full support item because the gold generation is the same regardless, as is the wards, and you need to focus on massive AP. You do need the second stage simply for the quest for the wards, and if you want you can get the final stage, but I personally prefer to save that money for stronger items.

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2. RUNES

Dark Harvest is godly with Veigar. Between your passive infinite stacking and Dark Harvest's infinite stacking, plus the percent-based multiplier of your AP added to DH, you can start getting a huge burst of extra damage. And it will refresh almost instantly if you kill the person, which you will likely do with the nutty damage you'll be dropping

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OVERALL - Literally everything about Veigar, and these builds specifically, give you the most insane late game imaginable. If you can stall long enough, you can single-handled turn any game around. And remember, even if you aren't stacking well early, you can easily start to come back with it. Just be sure early game you do your best to Q finish minions and poke your opponent when you can to get as many stacks as possible. You live for the stacks!

And remember, every 50 stacks 10% CDR is added to your W. Go long enough and you absolutely insane burst ability can be up constantly. So have fun and go nuts

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SUPPORTING

Support Veigar is viable when done normally. I in no way suggest my way is better than the standard, I have just had more personal success with it. The reasoning is, by upgrading abilities similar to Mid lane with slight exceptions, and by starting with Doran's, you can be a much more aggressive support than otherwise. Doran's gives more mana sustain, allowing you to Q poke and E zone way more.

I also suggest you focus on upgrading your Q because you want it off CD as much as possible. This allows you to apply greater pressure against the enemy, and as you get stacks from poking them, it will help you start your crazy stacking. If you're good, you can even potentially stack harder than when your mid lane, simply because you can focus purely on poking and not worry about waiting for CS opportunities with your Q.

I use the same rune page as Mid for the same reason - my Veigar support is a hard damage support. This allows us to have a backup plan should the ADC or our mid laner get shut down, Veigar support can be slowly but surely building up his snowball and turn the tide. His utility is more than enough for the team fights.

Also, don't be afraid to flash to get a well placed E. If you can pull it off and trap a number of enemies, giving your team some kills, it looks sick and turns the tide dramatically. Plus, worst case you get focused and your actually damage dealers are left alone to shred people. Win-win