Current GPUs rasterize micropolygons (polygons approximately one pixel in size) inefficiently. Additionally, they do not natively support triangle rasterization with jittered sampling, defocus, or motion blur. We perform a microarchitectural study of fixed-function micropolygon rasterization using custom circuits. We present three rasterization designs: the first optimized for triangle micropolygons that are not blurred, a second for stochastic rasterization of micropolygons with motion and defocus blur, and third that is a hybrid combination of the two. Our designs achieve high area and power efficiency by using low-precision operations and rasterizing pairs of adjacent triangles in parallel. We demonstrate optimized designs synthesized in a 45 nm process showing that a micropolygon rasterization unit with a throughput of 3 billion micropolygons per second would consume 2.9 W and occupy 4.1 mm2 which is 0.77% of the die area of a GeForce GTX 480 GPU. Categories and Subject Descriptors (according to ACM CCS): I.3.1 [Computer Graphics]: Graphics processors-I.3.7 Three-Dimensional Graphics and Realism.