We present a method to construct a patch of parametric surface of degree k + 1 that lls a n-sided hole, with n bigger than 2, and whose boundary coincides with a B-Spline, thus, the resulting patch can be easily connected with given B-Spline surfaces with xed continuity conditions. The method is inspired on a generic approach to construct free form surfaces, which gives a family of practical schemes to design surfaces from an arbitrary given mesh, using the di erentiable manifold theory. The input is a star shaped mesh which describes a generic n-hole and a surface in a neighborhood of the hole. The main advantages of the method are the following: arbitrary order k continuity conditions can be imposed; the involved hole can have an arbitrary number of sides and arbitrary shape (convex or not); the simplicity of the construction process gives an easy and exible method; and nally, the surface near the boundary is a B-Spline with piecewise uniform knot sequences and whose control points are vertices of the given mesh; both knot sequences and control points are easily computed. Implementation details to evaluate a surface point are given, showing that the de Boor algorithm can be exploited for efficiency.