A tile-based graphics processing system generates a render output by dividing it into a plurality of larger patches, each of which encompass a set of smaller patches. A rasterizer tests primitives against patches of the render output. When a primitive is found to completely cover a larger patch, depth function data for that primitive is stored in an entry of a depth buffer in respect of that largest patch position. When a subsequently-processed primitive is found to cover that same larger patch, the depth function data stored in the buffer is used to calculate depth range values for smaller patches that the larger patch encompasses. These depth range values, representative of the first primitive, are used to perform depth tests in respect of the second primitive. The depth function data stored in entry is then marked as invalid in respect of the smaller patches.