  This is the sequel to "Asymptotically Locally Euclidean metrics with holonomy
SU(m)", math.AG/9905041. Let G be a subgroup of U(m), and X a resolution of
C^m/G. We define a special class of Kahler metrics g on X called Quasi
Asymptotically Locally Euclidean (QALE) metrics. These satisfy a complicated
asymptotic condition, implying that g is asymptotic to the Euclidean metric on
C^m/G away from its singular set. When C^m/G has an isolated singularity, QALE
metrics are just ALE metrics.
  Our main interest is in Ricci-flat QALE Kahler metrics on X. We prove an
existence result for Ricci-flat QALE Kahler metrics: if G is a subgroup of
SU(m) and X a crepant resolution of C^m/G, then there is a unique Ricci-flat
QALE Kahler metric on X in each Kahler class. This is proved using a version of
the Calabi conjecture for QALE manifolds. We also determine the holonomy group
of the metrics in terms of G.
  These results will be applied in the author's book ("Compact manifolds with
special holonomy", to be published by OUP, 2000) to construct new examples of
compact 7- and 8-manifolds with exceptional holonomy. They can also be used to
describe the Calabi-Yau metrics on resolutions of a Calabi-Yau orbifold.
