A multi-pass method of generating an image frame of a 3D scene while eliminating the overdrawing of objects within the multiple graphics processing pipelines (GPPLs) supported on a parallel graphics processing system The GPPLs include a primary GPPL, and each GPPL, includes a color frame buffer and Z depth buffer. The GPPLs support an object-division based parallel graphics rendering process, in which the 3D scene is decomposed into objects that are assigned to particular GPPLs for processing. The multi-pass method involves, during a first pass, locally a Global Depth Map (GDM) which is provided to the Z depth buffer of each GPPL. This step involves the transmission of graphics commands and data for all objects in the image frame, to all GPPLs to be rendered. Then, during subsequent passes, a complementary-type partial image consisting of visible pixels only is generated within the color buffer of each GPPL using the GDM and a Z test filter supported by the Z depth buffer. After subsequent passes are performed, a complete color image is recomposited within the primary GPPL, using the complementary-type partial images stored in the color buffers of the GPPLs, without comparing or recompositing depth values in the Z depth buffers.