The 'Media Sharing' feature only allows devices (ie your laptop) access to your desktop's media. It does not mean that the files are being transferred to the laptop, at least not permanently.
If you want to transfer your library, then I'd suggest you get an external hard drive of some sort and copy & paste the media you want that's on your desktop to your laptop.
Since you probably want to keep the play-counts, ratings, skip-count, etc. of the files in your desktop's library, then you need to navigate to:
Find the file called MM.db
make a copy of that file onto the external hard drive, and place the file into same directory but in the laptop.
Doing this will transfer the information like ratings and such.
One problem you may face is that, if you then try to play a file on your laptop from it's MediaMonkey directory, it might not work. This is because the path to the file you want has changed.
To fix this, you've got two options. Both easy, really.
Probably the simpler method.
With MediaMonkey open on your laptop, highlight your entire library (click on a file in your library and press Ctrl+A), then go to File>Locate Moved/Missing Files...
Now simply direct MediaMonkey where to scan for those files, wherever they may it, and hopefully that'll be sorted.
If the first solution fails try this:
Say if on your desktop, all your music files were in a directory like this:
Then simply make it so that the directory is in the same position on your laptop. So you'd put your Music folder and place it in your desktop (this assumes you've got the same username on both your desktop and your laptop; if this isn't the case, place it somewhere else where the username of the computer does not show up in the directory)