Hockey Scenarios - Who gets the goal?

Suppose this happens:

It's the start of the game (so no prior player can possibly have touched the puck). For sake of point, it's Detroit-Colorado. Datsyuk and Sakic are the two centers taking the faceoff. Sakic wins it without Datsyuk getting a touch on it. Sakic passes it around his defence. The puck goes back eventually to Theodore. But he was feeling a bit dopey, and the puck ended up flying in the net. No Detroit player had touched the puck. So, who gets acredited with the goal? It cannot be a Sakic (or Theodore) own goal, because there's no such thing in Hockey. Does Datsyuk get it as the center?

Furthermore, what happens if Datsyuk got a bit excited before the faceoff, and got thrown out of the faceoff circle? This would put, say Zetterberg, in taking the face off. Sakic wins the faceoff and again the puck ends up in the Colorado net without anybody from Detroit touching it. Now who gets the goal? Zetterberg or Datsyuk? Or anybody else for that matter?

Would this change if there had been action prior to both of these faceoffs? Would it be the last Wing to touch it before the faceoff that gets the goal?

Whilst this is unlikely, it may happen if there's an empty net situation at the end of a game, and the attackers lose control of the puck and it goes flying into their own net, then this may actually happen/have happened.

I don't know the answer, by the way, this is just a question in a possible situation - it almost happened on NHL '06 (It was Aebischer not Theodore, and the puck hit the pipe).

So... If you can help, or direct me to somewhere that can help, I would appreciate it.