Components 38 (e.g., sensors 32) in devices 10A and/or 10B can monitor for device adjacency during the joint operations of block 64. For example, one or both devices may make sensor measurements to detect when devices 10A and 10B are pulled apart and/or wireless communications between devices 10A and 10B may be used in determining when devices 10A and 10B are no longer adjacent. So long as devices 10A and 10B are positioned so that devices 10A and 10B are adjacent (e.g., so that the edges of devices 10A and 10B abut one another in a side-by-side or overlapping arrangement) and a wired or wireless communications link is supported between devices 10A and 10B so that the control circuitry of devices 10A and 10B can share information and otherwise operate cooperatively to support joint operation, processing may continue at block 64, as indicated by line 66. In response to detecting that devices 10A and 10B have been separated, system 36 may transition from a joint operating mode (e.g., state 50-2 of FIG. 13) to an appropriate separate (independent) operating mode (see, e.g., states 50-3, 50-4, and 50-5 of FIG. 13). During the operations of block 68, it may be determined which, if any, of the operating settings from the joint state are to persist on each of the separate devices before operation loops back to the independent operations of block 60. As an example, if devices 10A and 10B were jointly displaying a web page during the operations of block 64, the web page may continue to be displayed on each device after device separation (e.g. each device may display a browser window with the same web page). As another example, if devices 10A and 10B were playing stereo music through respective first and second speakers in devices 10A and 10B, device 10A (but not device 10B) may continue to play the music through its speakers upon device separation. In general, all joint operating parameters may be retained when devices 10A and 10B are separated, some joint operating parameters may be retained, or no joint operating parameters may be retained.