Rented a movie last night from my computer (did not download the movie) with the hope I can watch it later on my Apple TV. I couldn't find the rented movie under "Purchased". Start researching and found this: https://support.apple.com/en-us/HT201611 If you rented the movie on your computer, but want to watch it on an iOS device, connect the devices and sync using USB. When you move a rented movie from your computer, it will disappear from your computer’s iTunes library. You can move the movie between devices as often as you want, but you can only have it on one device at a time. If you rented the movie on your iOS device or Apple TV, you can’t move it to any other device. I thought that, as long as I have NOT downloaded the rented movie, iTunes will recognize that there is a rented movie "pending" to be downloaded and I can download it once on ANY device I registered to.