  Branching processes pervade many models in statistical physics. We
investigate the survival probability of a Galton-Watson branching process after
a finite number of generations. We reveal the finite-size scaling law of the
survival probability for a given branching process ruled by a probability
distribution of the number of offspring per element whose standard deviation is
finite, obtaining the exact scaling function as well as the critical exponents.
Our findings prove the universal behavior of branching processes concerning the
survival probability.
