In this paper a new approach is presented to construct
piecewise polynomial G^k-surfaces of arbitrary topology and
smoothness order k>= 1 of degree O(k). This approach generalizes
some results presented in 1997 in CAGD and in 1999 at the St.
Malo conference, respectively. In our construction only 4n
polynomial patches are needed to fill an n-sided hole in a
generalized C^k-(half)-boxspline surface. This is achieved by
coalescing certain control points while at the same time
maintaining a regular parametrization.