This might be obvious to some now, but useful to know for new starters.
When you put a figure on the Infinity Base and its fresh out of packaging it will automatically take ownership.
Ownership of a figure sets the game to know you "own" that "character" and that figure of the character.
You start at level 0 and increase your experience up to level 15.
Ownership is tied to the game data/save and profile, for example the Xbox Gamertag save file or the Wii U user profile save data, or the PS3 local profile/PSN ID game save.
Hence if another profile tries to use the figure or you try to use the figure on a different format to the one you started on, or you take your figure and place it your friend's Disney Infinity, or you delete your data/save, it will come up as "Guest".
From the start menu you can take ownership of a figure in guest mode.
When should you take ownership or leave as guest? Simple.
For your profile and game save you should take ownership of your figures.
If you share a set of figures between family members using different profiles/IDs in the same household or on the same system but each wish to progress their figure separately and watch their hall of heroes grow etc. each player should take ownership.
One figure can be "owned" by multiple users at once, however each time you play you will need to retake ownership, especially to continue increasing its level.
So majority of the time take ownership?
Correct.
When should it be left as a guest?
As I see it, there's only one or two scenarios for leaving as a guest.
You've gone round to your friend's house and are playing Disney Infinity, you brought your figure along and you are player 2.
When you put your figure on your friend's Infinity Base it will be a guest.
While it is a guest, it will have its previous level and you can continue to level up, when you get home and put the character figure onto your base it will still be owned by you, but the level will have increased to what ever level you got it to as a guest on your friend's system, it then syncs this to your game data/save/profile.
If you had taken ownership on your friends game, it would likely have set him as the owner and reset to level 0 ready for him to start levelling it up on his save/profile. When you get home and retake ownership it will go back to level it was before you went over to your friend's house.
Another situation might be a shared family profile/game save, in which you use your characters as guests , so when back in your own profiles you can keep the experience gained there.
If you join in as player 2 while a family member is playing their game on their profile, leaving it as guest will allow you to keep the experience you gain for your character figure for later syncing to your game save, using take ownership will switch it for your family member to keep the experience gained for their character on their save data using your figure.
Note: Be sure to "bank" your experience earned as Guest so it's not lost.
You have used your figure in Guest mode on another profile/game system etc. and increased your figure level. You also share this figure with family members.
If you do not "bank" it before someone else takes or re-takes ownership, that experience you earned in Guest mode is lost, because taking ownership overwrites the figure with the current owner (most likely DI ID or Gamertag/PSN ID/Nintendo ID or could be a unique ID tied to the specific Disney Infinity save file) and level. This is why it flashes up a warning.
The current owner (you), needs to load up their Disney Infinity under their profile and place the figure on the base, it should still be owned by you and have the new level, the game will at this point write to your save file the character's new level.
Note: Any experience gained while the figure is owned by you playing on your own game save is automatically synced to your game data.
Yes that's right "taking ownership" simply writes your unique owner ID to the figure as well as what level it has for it in your game data, overwriting the previous owner and level.
If the character isn't listed in your game data yet, ie you've not used that character before, it sets it to level 0. Your figures levels are saved/synced in your game data, this is why a family can share one set of figures, they keep retaking ownership which "reloads" the figures with their data each time.
Q. What if I delete my game data/save?
A. All your figures will show up as Guests when you start a new game/data/save. Taking ownership will make them yours again and reset them to level 0. Only recommended if your game data/save has corruption.
Q. What if I lose a figure?
A. If you buy a replacement figure from a store, it will be blank (unused, unless it was used to demo) and like the first time you use a figure it auto takes ownership (hence all the people being confused about taking ownership since the game does it automatically on unused figures), same will happen except instead of starting at level 0, it will load the figure with the experience level you achieved before, it gets this from your game data/save.
If you buy a secondhand replacement from eBay, it will come up as a Guest, once you take ownership from the pause menu it will be yours and restore your experience level from your game data.
Q. What can I do to avoid data loss?
A. Take backup copies of your data, you can normally do this to a USB stick, cloud service (may require subscription) or possibly another profile.
Hope that clears it up.
Feel free to ask questions and I'll update the post.