MacOS – How to remove Preview.app on-screen navigation toolbar

Look at System Preferences > Mission Control and see if 'Automatically rearrange spaces based on most recent use' is checked.

When checked, fullscreen windows open to the immediate right.

When unchecked, fullscreen windows open at the far right, after all other desktop spaces.

You can also rearrange desktop spaces by dragging them to the order you prefer in Mission Control.

(I'm running 10.7.3)

Unfortunately, you can't. I am hoping Apple will fix this as soon as possible as well.

There's a trick where you can put some app in the fabric space, as documented in OS X hints.

However, if you utilize the full-screen swipe gesture to move to a separate full screen and pause/stop in the middle with multiple Spaces in view and invoke another application (i.e. via Spotlight), the spawned application can reside in the 'fabric space' or anywhere else. It basically remains attached to that space.