  Ahlfors Second Fundamental Theorem of covering surfaces over the Riemann
sphere are one of the major events in the history of function theory, which is
a geometrical interpretation of the famous Nevanlinna's Second Fundamental
Theorem in the theory of value distribution. The goal of this paper is to
present a method to identify the precise value for that constant h in Ahlfors'
SFT for covering surfaces over the unit sphere. This problem can be traced back
to the early 1940s, when J. Dufresnoy first gave a numerical estimate of h for
covering surfaces over a sphere. We will first prove the existence of extremal
surfaces, and then we will give a formula to compute the precise value.
