  We show that the limit laws of random matrices, whose entries are
conditionally independent operator valued random variables having equal second
moments proportional to the size of the matrices, are operator valued
semicircular laws. Furthermore, we prove an operator valued analogue of
Voiculescu's asymptotic freeness theorem. By replacing conditional independence
with Boolean independence, we show that the limit laws of the random matrices
are Operator-valued Bernoulli laws.
