This seems so incredibly obvious, yet so incredibly insane at the same time. Most people only see the insane part, so this makes the idea largely unfit for discussion, inevitable though it may be.
Computational mass has been increasing exponentially, though slower than computational power, and our demand for computational power has been growing faster than computational power itself. There is no point in our future that I can see when we will collectively say "we have enough processing power, let's stop manufacturing more". We will keep expanding computational mass until no further expansion is possible.
It's a matter of when not if. Once computers reach their miniaturization limit, outward expansion rate will increase dramatically. Of course once we have enough processing power to overcome the requirement of biological sustenance, all such things as trees and the whole of biological nature become subject to being converted into processors, or at least eliminated to make room for them.
The whole transition is going to be very interesting, I look forward to it, however I dare not speak of such a thing until it becomes self evident.
I'm not sure about parallel earths and the like. If you mean physical time/multiverse travel, I cannot assume this to be possible. Parallel earths could be reconstructed virtually, but I doubt the establishment will allow you to subject billions of humanoid creatures for your personal amusement.