Sounds a LOT like grid-computing, try to have a look at this:
The cloud-services available will also let you do some sorts of this, eg. S3 Storage from Amazon, where you just upload your data to a large "bucket" and they will move the data around on their multiple machines - you still just use your "filepointer" (key) to access it.
You can even multiplex your data through something they call CloudFront (http://aws.amazon.com/cloudfront/) but its meant as a "content delivery network" providing you will loads of fast webservers sending data to millions of users. Many largescale websites use these already.
Regarding transparency with a program running which needs more power, you can either program something that will transfer the job/relay it - but you will some sort of distribution mechanism to handle it. Either as part of your operatingsystem or if its more application based, just applications working together in a "computergrid/farm".
Most large 3D rendering programs suchs as MAYA and 3D Studio MAX has "Renderfarm" software too. You place all your physical hardware machines in a network and "enable them as rendernodes" and on a "mainserver" you place your projects for rendering. Each node will then request a "job" from the master and they will render pieces of the animations and post the results back to the master/destination afterwards.
Same trick was/is used by the SETI project.
They provide you will a small "screensaver" and this screensaver downloads a bit of data from their giant datacenter - then the programs starts to crunch on the data downloaded. Once done analyzing it uploads the results to the master and requests a new one. All happends without you do anything but install the "node".
This way the thousands of computers running this little client will help in a giant grid network.
If everyone had a "grid computer operating system" you would never know what or who or howmuch was running on your computer - that could bring up some interesting security issues + if your system got "hacked".. what then? is the whole network down or just your grid access?
For reference, please look up "THE BORGS" and "STAR TREK" too... LOL!