Well, this is a theory I created together with Elpizo, who is also a member of this forum, and based on some other theories whose authors I can't name for I don't know them. This is the first game theory I have ever posted, so I'm kinda nervous about it...
The theory is based on a facts and 2 suppositions. The facts were told to me by Elpizo. I don't know the sourses, so ask him.
Fact: The storyline in the world of Ivalice goes: FF XII => FF XII RW => FFT => Vagrant Story => FFTA => FFTA2
Supposition #1: Luso travels back in time
As far as we know, there are various races in FF XII and RW, and yet none of the races except humans are present in FFT. And leads to the
Supposition #2: Between the time periods of FF XII RW and FFT there was a catastrophe that wiped out all the races except humans.
That being said, I'll tell the theory itself (finally!):
All the Ivalices present in the game are one world, except the FFTA Ivalice.
As said in the supposition, a great catastrophe occured in Ivalice during the time between FF XII RW and FFT. A catastrophe that not only wiped out all the races except humans from the face of the planet, but also threw the human race from high developed technology back into medival one. The world continued to evolve the way it has become, eventually turning into the *real* Ivalice of FFTA, where Mewt buys an ancient book from a bookshop.
According to my theory, the book Mewt bought (called Gran Grimoire, I think) is a record/container of the wishes and dreams of those who got the chance to record them before the catastrophe.
This is proven by 2 facts: 1) Nono, who was just a simple mechanic, has his own airship now, and 2) Montblanc, who always wanted his clan to be the strongest one in Ivalice, makes his dream come true with assistance of Marche.
(Hardy didn't get a chance to record his dreams, poor little moogle

)
And so, Mewt bought the book that contains dreams and magic of the races that ceased to be. He reads the spell and activates the magic, resulting in the appearance of *dream* Ivalice. We see the entire place is transformed, and people are replaced by the 'dream' ones.
As we know, the Grimoire serves Mewt, in form of the Totema and Remedi and Llednar. It makes Mewt's dreams come true, along with the wishes of people close to him: his dad and his friends.
The corollary of the theory is that the people who vanish in the ending (instead of being replaced by their normal selfs) really vanish. For they are dreams and wishes, and we have destroyed Li-Grim, the essence of every wish ever made, the Crystals, the threads that bind the world, and the people who were also threads (Marche, Ritz, Mewt, Doned and Cid) have left it. And the Grimoire is probably left with blank pages, and/or with no magic at all...
In FFTA2, Luso also discoveres a book, but that one sends him back in time, to the Ivalice of FF XII - FFT time period. Which expains the presence of Vaan, Penelo, Al-Cid and other charachters from FF XII.
Well, that's all. If I have forgotten anything, or you have found some weak points in the theory, feel free to tell me.
Good comments will also be appreciated

Selena