The ability to run a 'second display' from the remote device requires software installed to 'fool' the desktop/computer OS into thinking it has another display connected. I do not know of any free option for this that is available for iPad.
AirDisplay works fairly well (better than the version of iDisplay I bought which was completely useless in real world application, so was the Wormhole Remote). After spending the cash on all three I was really upset to see how poorly they performed when they were purported to be a 'great option' for an added display. I felt really burned by the promise of good performance or features which were only partially delivered on what was advertised.
To be honest I haven't used AirDisplay much myself either, as I like to simply access the content I would have via native apps or the iPad Safari browser and not be 'tethered' to my desktop.
As for free apps, sorry.
The desktop osx app to do something similar (and its pretty cool, works well but not great for 'high framerates') is called ScreenRecycler and the companion vnc app called JollyFastVNC. I bet this developer could put together an iPad/iOS app for the same purpose.