  We study the uniformization conjecture of Yau by using the Gromov-Haudorff
convergence. As a consequence, we confirm Yau's finite generation conjecture.
More precisely, on a complete noncompact K\"ahler manifold with nonnegative
bisectional curvature, the ring of polynomial growth holomorphic functions is
finitely generated. During the course of the proof, we prove if $M^n$ is a
complete noncompact K\"ahler manifold with nonnegative bisectional curvature
and maximal volume growth, then $M$ is biholomorphic to an affine algebraic
variety. We also confirm a conjecture of Ni on the existence of polynomial
growth holomorphic functions on K\"ahler manifolds with nonnegative bisectional
curvature.
