  We compute all massive partition functions or characteristic polynomials and
their complex eigenvalue correlation functions for non-Hermitean extensions of
the symplectic and chiral symplectic ensemble of random matrices. Our results
are valid for general weight functions without degeneracies of the mass
parameters. The expressions we derive are given in terms of the Pfaffian of
skew orthogonal polynomials in the complex plane and their kernel. They are
much simpler than the corresponding expressions for symplectic matrix models
with real eigenvalues, and we explicitly show how to recover these in the
Hermitean limit. This explains the appearance of three different kernels as
quaternion matrix elements there in terms of derivatives of a single kernel
here. We compare to the Hermitean limit of complex matrix models with unitary
symmetry leading to some determinantal identities.
