  We study matricial approximations of master fields we constructed in a
previous work. These approximations (in non-commutative distribution) are
obtained by extracting blocks of a Brownian unitary diffusion (with entries in
$\mathbb{R}, \mathbb{C}$ or $\mathbb{K}$) and letting the dimension of these
blocks to tend to infinity. We divide our study into two parts: in the first
one, we extract square blocks while in the second one we allow rectangular
blocks. In both cases, free probability theory and operator-valued free
probability appear as the natural framework in which the limiting distributions
are most accurately described.
