A tessellation pipeline includes an alpha phase and a beta phase. The alpha phase includes pre-tessellation processing stages, while the beta phase includes post-tessellation processing stages. A processing unit configured to implement a processing stage in the alpha phase stores input graphics data within a buffer and then copies over that buffer with output graphics data, thereby conserving memory resources. The processing unit may also copy output graphics data directly to a level 2 (L2) cache for beta phase processing by other tessellation pipelines, thereby avoiding the need for fixed function copy-out hardware.