A set of user interfaces for a data processing system that operates with two or more display devices coupled to the system. In one embodiment, in response to moving a first window between two displays, the first window is displayed, as it straddles the two displays, differently on the two displays. For example, while a reference point (e.g. a cursor) on the window remains on a first display, a first portion of the window on the first display is displayed normally while a second portion on the second display is displayed with more translucence (more transparency) than the first portion; when the references point crosses to the second display, the first portion becomes more translucent than the second portion.