3rd party apps- what if you delete them?

I was just wondering, if you had a big iphone 3rd party app that you wanted to delete to make room for other apps, would you have to buy it again, or would it be saved to your mac to manage them when you sync. I know you can download them on itunes and sync them, but does it work the other way round i.e. you download them on the app store and then they are copied to your mac to be saved.

Since nobody has really taken a stab at the App Store, it would be safe to assume that some sort of record is kept as to what applications you have bought in case you ever need to reload them, such as following a restore or replacement.

Well, when you purchase music on the iPhone it syncs back to your computer. When you buy a movie on your Apple TV it syncs back to your computer. So lets hope Apps do to...