Is there a way to prevent downloads of purchased items to iTunes?

1. Open iTunes
2. Click iTunes Store
3. Go to the iTunes Store Home
4. On the right column is the text "Purchased" with a little bubble that says (new). Click "Purchased"
5. Find the show that you don't want.
6. Click it and then a window should pop up containing the show
7. There should be an (X) next to the show. Click That
8. iTunes will ask you whether you want to make the show hidden. You do.
9. Repeat for all other shows.

There is no way to designate one specific purchased item to not auto-download and remain in the cloud, but you can specify certain kinds of purchased items like videos, music, books, etc.

In iTunes > Preferences > Store Preferences on your computer, make sure to uncheck "Always check for available downloads" and "Automatically download pre-orders".

Initiate the purchase on a device other your computer. The simplest way would be to initiate the purchase on a Apple TV, as those purchases will now remain in the cloud and not auto-download to iTunes on your computer.

Same here, purchased on ATV3 and not showing up in my itunes as a purchase - but constantly starting the download after a login on itunes. I switched all auto downloads off and even shut off TV Series and Movies on my itunes to show up - still did not help...