Why is everyone making this more complicated than it is?
Amnesiac, do the following:
1. Copy the Mad Men episodes to her computer and import them into her iTunes program. (You can do this using a memory stick, or by entering your account information in her iTunes and downloading the episodes from the "purchased content" section.)
2. Open one of the episodes in her iTunes program. If/when prompted, authorize your girlfriend's computer for material from your iTunes account.
Done.
This is all within the iTunes terms of service. It is a personal, noncommercial use, and there are no legal problems with doing it.
See here:
http://www.apple.com/legal/itunes/us/terms.html#SERVICE
To clarify:
You get 5 authorized devices (at one time) that can play your purchased iTunes content. Period. So all you have to do is authorize your girlfriend's computer to play the content and you are fine.
Nowhere in the iTunes terms of service does it say anything about requiring that the 5 authorized devices be in your home, or that you be the owner of these 5 devices. None of this "pay her a dollar so that it's your computer" nonsense is even theoretically required. You don't even have to de-authorize her computer when you leave, if you don't want to. (It's just that you will have one less free device you can authorize to play your purchased content until you de-authorize her computer.)
Playing the videos from your iPhone using an Apple TV or an RCA/Component adaptor would work too, but it's not necessary and I wouldn't recommend you buy anything just for the purpose of getting to watch the shows on her computer. You already have everything you need to do that (your iTunes account and the episodes themselves). You can just copy the content to her computer's iTunes library as long as her computer is one of your iTunes account's authorized devices.
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YOU DON'T HAVE TO DO THIS. See my previous post.
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I don't think this is true. Can you point me to where this is stated? I can't find it in the iTunes terms of service.
Or are you saying this is written in some intellectual property law somewhere, and is not mentioned in the iTunes terms of service?
(I'm willing to be proven wrong.)