This my understanding supported by some experimentation.
I think the free mobile versions need to be online to access and create maps. They use Connect as their file store.
You can connect to the Connect file store from MindManager 2012. You have the choice of storing maps there or on your local/network drives and of course making copies (I would).
Either application can edit maps stored on Connect. You can also share 2 maps at a time with others for editing. You can let other users view but not edit all the maps on Connect.
However I have experienced maps being locked from editing when I think shouldn’t be and problems with saving maps after editing.
Mindjet say the take up of the free products has exceeded their expectations and they are addressing the issues this has raised.