  The free Meixner laws arise as the distributions of orthogonal polynomials
with constant-coefficient recursions. We show that these are the laws of the
free pairs of random variables which have linear regressions and quadratic
conditional variances when conditioned with respect to their sum. We apply this
result to describe free Levy processes with quadratic conditional variances,
and to prove a converse implication related to asymptotic freeness of random
Wishart matrices.
