Odd smoking problem, S5 T2.
 

About a month ago, my car decided to start smoking like a smoke stack on cold start, but when I drove it for about 20-30 seconds it would stop smoking COMPLETELY. The smoke was white, and didn't smell sweet, but more like a burning smell.

After a few days of this and some research, I decided to swap in my spare turbo I had in the spare parts collection.

Now, this is where it gets odd. It no longer smokes on cold start, except for a tiny tiny puff right when it kicks over. About a minute into it running, it starts smoking just a little out of the exhaust, about 1/10th the volume it was before(Same smell, same color), but now it is smoking from the turbo as well, just a tiny tiny bit.

The engine idles fine during this whole process.

I'm leaning towards this turbo also being bad, but this being my first T2, I'm working off research alone.

Yes, that sounds like a turbo with a blown seal. Oil can leak into the compressor or turbine side, and both will cause smoking. I'd lean towards a compressor side leak if the smoke eventually went away. If the "new" turbo also smokes, it's probably on the way to the same fate. I'd double check the oil lines to be sure they're not leaking at all, which could also cause smoke.

I've checked all the lines a few times.

Before, I thought it was an oil control ring, as the the turbo was leaking copious amounts of oil.

The fact that one turbo smokes while hot, and one smokes while cold is a little odd to me.