  The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility
of obtaining a discontinuous (explosive) percolation transition by changing the
stochastic rule of bond occupation. Despite the active research on this
subject, several questions still remain open about the leading mechanism and
the properties of the system. We review the largest cluster and the Gaussian
models recently introduced. We show that, to obtain a discontinuous transition
it is solely necessary to control the size of the largest cluster, suppressing
the growth of a cluster differing significantly, in size, from the average one.
As expected for a discontinuous transition, a Gaussian cluster-size
distribution and compact clusters are obtained. The surface of the clusters is
fractal, with the same fractal dimension of the watershed line.
