[Voronwe]

Just one point: although the elves were immortal no matter what, as lathspell pointed out, elves who remained in Middle Earth after the 3 rings lost their power and the dominion of Men began did fade. There are many mentions of this, for example by Galadriel, in the Doom of Mandos, and in the narrative of the Silmarillion. It seems that it was part of the fate of Arda that the Elves who remained in Middle Earth would 'fade', becoming less potent and living more and more in memory, while the younger race of Men would take dominion of Middle Earth.

The 3 Rings of the Elves had the power the postpone this fading and weariness of Middle Earth, which is why when the One Ring was destroyed and the 3 Rings lost their power many of the Elves sailed West. The fading was not caused by the rings, but the rings once possessed the power to postpone the fading.