Full exploitation of the sophisticated physical modeling capabilities of computational fluid dynamics has been hampered by the inability to generate high quality grids in a timely manner. Complex geometries further exacerbate grid generation difficulties. Despite the potential for fully automatic grid generation with the relatively new unstructured techniques, such a capability has, in large part, remained elusive. The principle difficulty with the generation of such grids lies within the surface discretization, the operation for which, though difficult in its own right, must be intimately coupled with CAD data to retain geometric integrity and achieve the desired efficiency. This paper presents a new method for generating high quality unstructured surface grids directly on NURBS surfaces or any other surface for which a similar parameterization exists; surface distributions are automatically adapted to local curvature which renders a high fidelity representation of the geometry with optimum use of grid points. The method is applied to numerous surfaces possessing large variations in curvature to demonstrate its effectiveness at producing high quality surface grids automatically.