With iTunes, you an export a playlist and import it into a different computer in order to have the same playlist in both places.
You must also copy the songs (or better yet, copy the entire artist folder containing the songs, to keep the songs organized) in order for the playlists on the other computer to work. Exporting a playlist does not copy the songs in the playlist. You get a list of songs in the XML (eXtensible Markup Language) format, but not the songs themselves -- you still need to copy the actual songs files to the other computer.
To export a single playlist, select the playlist and choose File, Export Song List. On a Mac, choose the XML options from the Format pop-up menu in the Save: iTunes dialog box, and click the Save button. In Windows, choose the XML option from the Files drop-down menu in the Save window.
After exporting a playlist and copying it to another computer, you can import the playlist into iTunes on the other computer by choosing File, Import on that computer, selecting the XML file, and clicking the Choose button. You can also export all the playlists in your library at the same time by choosing File, Export Library; then import them into iTunes on the other computer by choosing File, Import and selecting the exported XML file.
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