[lbj]

If the app was downloaded first to the phone, it will automatically download to your home computer when you sync. Provided your home computer is the one you normally sync to.

Your work set-up has me confused and I'm wondering if, in reality, you are synced to your work computer which is why you get the 'erase all' message when you try and sync at home. Or have I misunderstood you?

To download the app to your home computer, launch iTunes, go to the store, search for the app, then download. There are two ways to get apps on the iPhone, either directly on the phone or via your iTunes on your synced computer.