  This paper is an adaptation of a method used in \cite{K} to the model of
random quadrangulations. We prove local weak convergence of uniform measures on
quadrangulations and show that the local growth of quadrangulation is governed
by certain critical time-reversed branching process and the rescaled profile
converges to the reversed continuous-state branching process. As an
intermediate result we derieve a biparametric generating function for certain
class of quadrangulations with boundary.
