  In the study of the constant in Ahlfors' second fundamental theorem involving
a set E_{q} of q points, branch values of covering surfaces outside E_{q} bring
a lot of troubles. To avoid this situation, for a given surface S, it is useful
to construct a new surface So such that L(So) <=L(S), and H(S)>=H(S), and all
branch values of So are contained in E_{q}. The goal of this paper is to prove
the existence of such So, which generalizes Lemma 9.1 and Theorem 10.1 in Zhang
G.Y.: The precise bound for the area-length ratio in Ahifors' theory of
covering surfaces. Invent math 191:197-253(2013)
