  We study asymptotic percolation as $N\to \infty$ in an infinite random graph
${\cal G}_N$ embedded in the hierarchical group of order $N$, with connection
probabilities depending on an ultrametric distance between vertices. ${\cal
G}_N$ is structured as a cascade of finite random subgraphs of (approximate)
Erd\"os-Renyi type. We give a criterion for percolation, and show that
percolation takes place along giant components of giant components at the
previous level in the cascade of subgraphs for all consecutive hierarchical
distances. The proof involves a hierarchy of random graphs with vertices having
an internal structure and random connection probabilities.
