  We consider a generalized model of repeated quantum interactions, where a
system $\mathcal{H}$ is interacting in a random way with a sequence of
independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness
are studied in detail. One is provided by considering Haar-distributed
unitaries to describe each interaction between $\mathcal{H}$ and
$\mathcal{K}_n$. The other involves random quantum states describing each copy
$\mathcal{K}_n$. In the limit of a large number of interactions, we present
convergence results for the asymptotic state of $\mathcal{H}$. This is achieved
by studying spectral properties of (random) quantum channels which guarantee
the existence of unique invariant states. Finally this allows to introduce a
new physically motivated ensemble of random density matrices called the
\emph{asymptotic induced ensemble}.
