This paper presents a method for generating computational meshes by building structured component grids and then connecting them with an unstructured mesh. The approach uses technologies from the overset grid community, specifically the Ogen overlapping grid generator from the Overture framework, to build a collection of overlapping structured grids for a given geometry. Overlapping regions between the component grids are automatically removed and replaced with an unstructured mesh that conforms to the boundaries of the holes in the structured grids. Large regions of high-quality structured grids comprise most of the domain and are connected by a comparatively small amount of unstructured mesh. A method for generating hybrid surface meshes from overlapping and intersecting surface grids is also described. These surface meshes preserve the geometry used to generate the structured grids by querying the original geometry database. An implementation of advancing front mesh generation creates the interstitial surface and volume unstructured meshes. Mesh spacing information is automatically computed from the original overlapping grid. The mesh is optimized by regeneration in areas of poor quality as well as vertex repositioning by non-linear optimization of a quality metric. Quality assessment is accomplished by incorporating the mesh spacing information into algebraic mesh quality metrics. A description of the approach and algorithms is presented followed by two- and three-dimensional demonstrations. Published in 2004 by John Wiley & Sons, Ltd.