I like MINKIN2's suggestion of picture-in-picture: one app full screen with full controls, and one app shown as thumbnail without controls (watch only). It is not as powerful as the ability to control 2 apps running side by side, but may better accommodate smaller screens (laasonen concern). MINKIN2, I have added this idea to the brainstorm and credited you - hope you don't mind Maybe you should patent it!


The PIP mode provides the ability to perform a task within fullscreen app, while monitoring a status or an even within the inset app.
Here are few possible inset app:
- video chat / video stream: e.g. you write an email while watching live TV
- social updates (notifications): e.g. you want social updates to be always displayed on the screen
- turn by turn games like chess: e.g. you browse the web while your opponent is thinking of the next move

Interaction:
- you enter the PIP mode from the open application view by drag-and-dropping the thumbail of one app (A) into the thumbail of another app (B): the result is app A fullscreen, full controls, with app B displayed as inset
- all inputs are directed to fullscreen app, except:
+ taps into inset app: these taps make both apps switch roles, inset app becomes fullscreen, fullscreen app becomes inset
+ finger dragging within inset app: these drags makes the inset app move within the screen. this feature enables to place inset app anywhere within the screen
+ pinch-to-zoom within the inset app: these gestures makes the inset app thumbnail smaller or bigger (within limits such that it remains always clear which app is inset, which app is fullscreen)
- you leave the PIP mode by swiping the main application out (regular interaction to leave an app)

Pros:
- should be easier to implement than a a tiling system
- should be less confusing to the user than a tiling system

Cons:
- only the fullscreen app receives input, it is not possible to control 2 apps at the same time. This multitasking presentation is appropriate when doing one task and monitoring a status.
- the full screen app will draw its view regardless of the inset app, which is not efficient
- the inset app will mask part of the fullscreen app view - this issue is however mitigated by the fact that the inset app thumbnail can be moved