In a tile-based graphics processing system having plural rendering processors, the set of tiles 31 to be processed to generate an output frame 30 for display is partitioned among the different rendering processors by defining respective tile traversal paths 32, 33, 34, 35 for each rendering processor that start at a tile initially allocated to the processor and that, at least for the initial tiles along the path, traverse to spatially adjacent tiles in the output, and that will traverse every tile to be rendered if followed to their end. The next tile for a given rendering processor to process is then selected as being the next tile along its defined path, unless the next tile in the path has already been processed (or is already being processed) by another rendering processor, in which case the next tile to be allocated to the rendering processor is selected to be a free tile further on in the tile traversal path for that processor.