I use AirServer to mirror my iPad to my MBP. The caveats are
- It requires that your iPad and computer be on the same WiFi network (IOW you must have WiFi on the desktop even when hardwire ethernet may be faster)
- It requires that your WiFi routers support Bonjour services (this has recently become an issue with upgrades done to my work network)
- The desktop version does not support split screen (I have a feature request in on this because it will be useful to project a presentation in one split screen and show annotations being done on the iPad [with ZoomNotes] in a second split view)
As for doing the reverse (using the iPad as an extra monitor), see the discussions here about the LunaDisplay.
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JJW