To fill an N-sided hole on a NURBS surface and to blend a corner formed by NURBS surfaces, we propose a regular N-sided open uniform quadratic subdivision surface derived by applying the open uniform quadratic subdivision scheme to a regular N-sided control mesh which is confined to the hole or to the region of the vertex blend. Boundary conditions such as C0 and G1-continuity required for the hole filling and vertex blending, are ensured by certain refinement steps performed in the course of the subdivision. The shape of the filling or blending surface is controlled by using fullness parameters. Methods are also proposed to represent the resulting regular N-sided open uniform quadratic subdivision surface using non-uniform rational B-spline surfaces.