I know that there is no way of auto adding the JQuery Mobile App to the Home Screen.
I\'ve read that the best way is to detect if the app is in full screen and if no
You can not 'Auto Add' as webapp to your home screen, the only option is thing: http://www.tuaw.com/2008/12/19/iphone-101-add-mobile-websites-to-home-screen/
Note: Auto Adding a webapp to your homescreen would be a really bad thing, just think any webpage you went to could auto add itself to your iphone. NO THANKS!!!
UPDATE:
I think this is what you're looking for: http://code.google.com/p/mobile-bookmark-bubble/ I have made a Feature Request (under new widgets) for this: https://github.com/jquery/jquery-mobile/wiki/Feature-Requests
Related Links:
Maybe Notification Popup? - How to show the "add to home screen" popup window and notifications like the buildin home? - Is there a JQuery plugin for the iPhone that will notify the user to "Bookmark" their app?