  We develop an analytic theory of operator-valued additive free convolution in
terms of subordination functions. In contrast to earlier investigations our
functions are not just given by power series expansions, but are defined as
Frechet analytic functions in all of the operator upper half plane.
Furthermore, we do not have to assume that our state is tracial. Combining this
new analytic theory of operator-valued free convolution with Anderson's
selfadjoint version of the linearization trick we are able to provide a
solution to the following general random matrix problem: How can we calculate
the asymptotic eigenvalue distribution of a polynomial evaluated in independent
random matrices with known asymptotic eigenvalue distributions?
