  The partition function of the finite $1+\epsilon$ state Potts model is shown
to yield a closed form for the distribution of clusters in the immediate
vicinity of the percolation transition. Various important properties of the
transition are manifest, including scaling behavior and the emergence of the
spanning cluster. The predictions are compared with simulations. Agreement is
found to be good, although convergence between theory and numerical results as
the system size is increased is, in some cases, unaccountably slow.
