The children of Elrond and their choice?

[Knight of Gondor]

In the Return of the King appendices (which, by the way, are an EXCELLENT introduction to the massive histories of Middle-Earth without/before reading The Silmarillion), in Appendix A, The Númenorian Kings, the book states that the Valar gave Elrond and Elros the choice to be mortal or immortal. Of course, we know who chose what. But then it goes on to state that the Children of Elrond were given a choice also to remain and become mortal and die in Middle-Earth, or to go with him from the circles of the world. Is there no third option? Was it either stay and die, or go and live?

I guess this also brings to mind the question of the future; what finally happens after Aragorn’s death? The books very clearly indicate that Men were coming into power the most on the earth. Does this mean that all the Elves left Middle-Earth, eventually? What about dwarves and hobbits? They aren’t “Men” per se, do they diminish too? What happens after the events of the War of the Ring?