I left the application on my main computer, then moved the library to an external hard drive. I have two externals, so I occasionally back the library up from one to the other. (I use chronosync for this.)
Hope this helps! I put my itunes library on the external, too. My computer has only a 20 GB drive (it's four years old), with part of that partitioned off for OS9, so space was really, really an issue. Having those two libraries on the external helped tremendously.