  We show that the surface roughness for $c<1$ matter theories coupled to $2D$
quantum gravity is described by a self-similar structure of baby universes.
There exist baby universes whose neck thickness is of the order of the
ultraviolet cutoff, the largest of these having a macroscopic area $\sim A^{1
\over {1-\gamma}}$, where $A$ is the total area and $\gamma$ the string
susceptibility exponent.
