  We study a fragmentation problem where an initial object of size x is broken
into m random pieces provided x>x_0 where x_0 is an atomic cut-off.
Subsequently the fragmentation process continues for each of those daughter
pieces whose sizes are bigger than x_0. The process stops when all the
fragments have sizes smaller than x_0. We show that the fluctuation of the
total number of splitting events, characterized by the variance, generically
undergoes a nontrivial phase transition as one tunes the branching number m
through a critical value m=m_c. For m<m_c, the fluctuations are Gaussian where
as for m>m_c they are anomalously large and non-Gaussian. We apply this general
result to analyze two different search algorithms in computer science.
