  In invasion percolation, the edges of successively maximal weight (the
outlets) divide the invasion cluster into a chain of ponds separated by
outlets. On the regular tree, the ponds are shown to grow exponentially, with
law of large numbers, central limit theorem and large deviation results. The
tail asymptotics for a fixed pond are also studied and are shown to be related
to the asymptotics of a critical percolation cluster, with a logarithmic
correction.
