TARDIS Flash Drive

Hey this is my first post, so here is my question: is there a way to make a thumb drive so that when you save something to it it saves the file to a remote disc, so if i had a 2GB thumb drive and i plugged it into a computer at the library I could save a 10 GB file to it and the file would save to my disc at home, and I would also be able to then plug the same thumb drive into a different library computer and open this 10 GB file. The idea is it would function as a normal flash drive and you wouldn't have to istall a program onto each new computer you use the flash drive with. Does this kind of thing exist? Could it be made? How? What would it involve

(TARDIS because the drive would be bigger on the inside)

It wouldn't only be cool but it would be an amazing tool to have especially for graphic designing when you always have to back stuff up and it often too big for a thumb drive. Also you can't loose it because all the files are at home.

Uhh, use Dropbox or any of the various cloud storage derives as your remote disk and get the account that matches your need.

I mean that I would own the drop box, no company storage facility, and that you wouldn't have to open a drop box application in the flash drive, files would simply be transferred to the disc at my house.

No such thing exists..

Why not just go out and get an OWC Express Black Portable External Hard Drive Enclosure down load what you need at the library and be done with it.