  Distributions of the size of the largest component, in particular the
large-deviation tail, are studied numerically for two graph ensembles, for
Erdoes-Renyi random graphs with finite connectivity and for two-dimensional
bond percolation. Probabilities as small as 10^-180 are accessed using an
artificial finite-temperature (Boltzmann) ensemble. The distributions for the
Erdoes-Renyi ensemble agree well with previously obtained analytical results.
The results for the percolation problem, where no analytical results are
available, are qualitatively similar, but the shapes of the distributions are
somehow different and the finite-size corrections are sometimes much larger.
Furthermore, for both problems, a first-order phase transition at low
temperatures T within the artificial ensemble is found in the percolating
regime, respectively.
