  An $k$-noncrossing RNA structure can be identified with an $k$-noncrossing
diagram over $[n]$, which in turn corresponds to a vacillating tableaux having
at most $(k-1)$ rows. In this paper we derive the limit distribution of
irreducible substructures via studying their corresponding vacillating
tableaux. Our main result proves, that the limit distribution of the numbers of
irreducible substructures in $k$-noncrossing, $\sigma$-canonical RNA structures
is determined by the density function of a $\Gamma(-\ln\tau_k,2)$-distribution
for some $\tau_k<1$.
