The Wii U's success really has little to do with the XBox One or the PS4. If the Wii U can get quality software that takes advantage of its features, it succeeds. If not, it fails.

No, because the eventual Xbox One support wont go to Wii U, it will go to the PlayStation 4.

The Wii U's problems arent the competition, its the complete lack of worthwhile games for long periods of time. The Wii U needs games. No matter what happens to the competition, the Wii U will continue to struggle without meaningful support.

In the scenario that xbox leaves the market, yes. Wii U would benefit from it. It would ciment its position as the console for those that dont want the ps4 or want something more.
3rd party developers would be forced to review their strategies and multi plats would probably be more common. 3rd parties cant afford to put all their cards on Sony cause that would put Sony in a gigantic position of power. Overall it would dominate ofc.

In the scenario that xbox simply sells as much as the first one, little will change... except microsoft would be losing rivers of money again.

Not true. The competition could just get tired of trying and end up stopping production.

Actually, that probably won't help either.

If the X1 fails WiiU will fail even harder.
One of the reasons why the X1 failed will be the lack of power. So people will not jump to an even more inferior system with even less games.

It couldn't even flourish on its own for an entire year. It's just a trash console with trash games.

There's actually a precedent for people doing exactly what you say won't happen.

It's called the 6th gen ( where the PS2 was the One to rule them all )...

Wii U has, imo completely different market. They aim for a younger audience than the other two.

If X1 goes down I would expect its playerbase to move to either affordable PC gaming/steambox (if anti-sony) or just PS4 instead of Wii U.

Wii U drastically weaker than the PS4 so you would get low quality ports at best, possibly with some cut content. Unless ofcourse developers start gimping their games which I dont see happening.

If Xbox One fails, developers like 343 Industries, Turn 10, and Black Tusk are far more likely to go to Sony than Nintendo.

If Xb one truly fails, i.e. gets taken off the market, then yes, some people will go to Wii U. But PS4 would benefit more. And lots of people just won't bother with consoles.

But yes, if 3rd parties can't make enough money from a dominant PS4 and a failed, but still on the market, Xb one, then they will release games on Wii U to try to get every last possible sale. The cost of making a decent Wii U port should be cheap enough that just a few hundred K sales on Wii U will be profitable. And more 3rd party multiplatform games on Wii U, with Xb one being a bit of a turn off should help Wii U to sell somewhat better.

But "flourish" might be a bit strong of a word.