The probability distribution of the largest cluster size is studied within a three-dimensional bond percolation model on small lattices. Cumulants of the distribution exhibit distinct features near the percolation transition (pseudocritical point), providing a method for its identification. The location of the critical point in the continuous limit can be estimated without variation of the system size. This method is remarkably insensitive to finite-size effects and may be applied even for a very small system. The possibility of using various measurable quantities for sorting events makes the procedure useful in studying clusterization phenomena, in particular nuclear multifragmentation. Finite-size scaling and \ensuremath{\Delta}-scaling relations are examined. The role of surface effects is evaluated by a comparison of results for free and periodic boundary conditions.
We examine the average cluster distribution as a function of lattice probability for a very small
(L=6) lattice and determine the scaling function of three-dimensional percolation. The behavior of the second moment, calculated from the average cluster distribution of
L=6 and
L=63 lattices, is compared to power-law behavior predicted by the scaling function. We also examine the finite-size scaling of the critical point and the size of the largest cluster at the critical point. This analysis leads to estimates of the critical exponent $\ensuremath{\nu}$ and the ratio of critical exponents $\ensuremath{\beta}/\ensuremath{\nu}$.