  Orthogonal - unitary and symplectic - unitary crossover ensembles of random
matrices are relevant in many contexts, especially in the study of time
reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal
polynomials we show that the same generic form of n-level correlation functions
are obtained for the Jacobi family of crossover ensembles, including the
Laguerre and Gaussian cases. For large matrices we find universal forms of
unfolded correlation functions when expressed in terms of a rescaled transition
parameter with arbitrary initial level density.
