  In this work, we describe the asymptotic behavior of complete metrics with
prescribed Ricci curvature on open Kahler manifolds that can be compactified by
the addition of a smooth and ample divisor. First, we construct a explicit
sequence of Kahler metrics with special approximating properties. Using those
metrics as starting point, we are able to work out the asymptotic behavior of
the solutions given in the work of Tian-Yau, in particular obtaining their full
asymptotic expansion.
