How are file permissions handled on external media and other computers?

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http://www.linuxquestions.org – I was wondering, what if you had a flash drive formatted with an FS that has UNIX permissions. Then what if you copied some of your files onto it. And then put it into another computer that has a user account by the same name. WIll the user be able to access the files? What if you named your own user differently on the other computer, will you be able to get your files? What about tar archives? (HowTos)