1. A method of performing graphics processing using parallel geometry processing engines, comprising: receiving a serial input stream identifying vertex indices and at least one command for generating primitives; performing an initial stage of primitive assembly before slot assignment of vertex information and utilizing the initial stage of primitive assembly to construct independent batches of work for downstream vertex and geometry processing in independent parallel processing units that each include respective buffer memories that do not share vertex information, each independent batch of work corresponding to a complete list of vertices for a set of primitives with the total number of vertices being less than or equal to a maximum pre-selected number of vertices; and writing said independent batches of work to said independent processing units, wherein each batch is written into slots of a buffer of an available independent processing unit for at least one of vertex shading and geometry processing.