What happens if I buy a game I own on Uplay, on Steam?

I just did this. I have Assassin's Creed 3 on Uplay from a free download code when I got a gfx card a few years ago. I just bought AC3 on steam during the winter sale and now my Uplay account shows two instances of AC3, one of them is the uplay version that tries to download it from the Uplay servers and the other one is a link that starts the steam version.

If you buy a Uplay game on Steam that you already own on Uplay, you will now own the game on Steam as well. This means you can install the game from Steam. You can then launch the Steam specific version through the Steam launcher.

Uplay games generally require you to sign into a Uplay account--- even when owned on Steam and launched through Steam. This means you have 2 DRM levels for Uplay games that you play through Steam--- the normal Steam level, plus having to then authenticate with Uplay.

If you desire, you can create a new Uplay account and use that account to play your Steam game. Or you can simply use your existing Uplay account when you launch the Steam version of the Uplay game you already own. So you can make life as complicated or as simple as you like.

If you make a new Uplay account, be prepared to provide CD Key information on the Steam game you purchased. This will tie the game to the new Uplay account.