FIG. 7 shows the software driver for operating a modification of the hardware shown in FIG. 6. In FIG. 7, only two hardware buffers 12.sub.1 and 12.sub.2 are used. In the specific case illustrated, a micro computer connected to a host computer is assumed with buffer 12.sub.2 being the micro computer buffer, but it will be understood by those skilled in the art that the technique applies also to a single computer provided there is sufficient system memory. As shown, this implementation employs screen control blocks 32, window control blocks 34, presentation space control blocks 36, presentation spaces 38, and a screen matrix 40. There may be, for example, ten screen control blocks and ten sets of window control blocks, one each for each screen layout. A given screen control block 32 points to a corresponding set of window control blocks 34. Each presentation space 38 has at least one window per screen layout. The presentation spaces, but not the windows, are common to all screens. The window control block 34 corresponding to a given presentation space 38 in that screen layout defines the origin (upper left hand corner) of the window in the presentation space, the origin of the window on the display screen, and the width and height of that window in the presentation space. The screen matrix 40 is a map of the data to be displayed and, in one embodiment, maps on a one for one basis the characters that can be displayed on the CRT screen, but the mapping could be on a pel basis or any other basis. All application output from the several tasks is directed to memory and specifically to the presentation spaces 38 rather than the hardware refresh buffer. In FIG. 7, a micro computer such as the IBM Personal Computer (PC) is assumed to be attached to a host computer such as an IBM 3270 computer via a controller such as an IBM 3274 controller. For this case, the PC hardware buffer 12.sub.2 acts as the PC presentation space. Each presentation space is assigned an identification tag and has an associated window defined by the operator or an application program as to size and screen location. When the operator or an application program adjusts the windows relative to one another, the system builds an image in the screen matrix 40 consisting of the identifying tag aligned in the appropriate locations. The matrix 40 may be created in a reverse order from that appearing on the CRT screen allowing overlapping windows to be built up by overwriting. Alternatively, by using a compare function, the matrix 40 can be created by beginning with the top window. The choice of the method of creating the matrix 40 is based on desired system performance. The system directs output to the refresh buffer by filtering all screen updates through the screen matrix 40, allowing a performance increment in an overlapped window system by only allowing those characters that actually need to be reflected on the screen to be so, and those that do not, will not cause an unnecessary redraw. The absence of these unnecessary redraws removes the requirement for continual updates of all windows whenever the contents of one is altered (col. 5, ln 7-64).