  By work of Jenkins and Strebel, given a Riemann surface X and a simple closed
multi-curve $\alpha$ on it, there exists a unique quadratic differential q on X
whose horizontal foliation is measure equivalent to $\alpha$. We study the
distribution of the critical graphs of these differentials in the moduli space
of metric ribbon graphs as the extremal length of the multi-curves goes to
infinity, showing they equidistribute to the Kontsevich measure regardless of
the initial choice of X.
