  The differential systems satisfied by orthogonal polynomials with arbitrary
semiclassical measures supported on contours in the complex plane are derived,
as well as the compatible systems of deformation equations obtained from
varying such measures. These are shown to preserve the generalized monodromy of
the associated rank-2 rational covariant derivative operators. The
corresponding matrix models, consisting of unitarily diagonalizable matrices
with spectra supported on these contours are analyzed, and it is shown that all
coefficients of the associated spectral curves are given by logarithmic
derivatives of the partition function or, more generally, the gap probablities.
The associated isomonodromic tau functions are shown to coincide, within an
explicitly computed factor, with these partition functions.
