  Recently, the modified BFW model on random graph [Phys. Rev. Lett., 106,
115701 (2011)], which shows a strongly discontinuous percolation transition
with multiple giant components, has attracted much attention from physicists,
statisticians and materials scientists. In this paper, by establishing the
theoretical expression of evolution equations on the modified BFW model, the
steady-state and evolution process are analyzed and a close correspondence is
built between the values of parameter \alpha and the number of giant components
in steady-states, which fits very well with the numerical simulations. In fact,
with the value of \alpha decreasing to 0.25, the error between theoretical and
numerical results is smaller than 4% and trends to 0 rapidly. Furthermore, the
sizes of giant components for different evolution strategies can also be
obtained by solving some constraints derived from the evolution equations. The
analysis of the steady-state and evolution process is of great help to explain
why the percolation of modified BFW model is explosive and how explosive it is.
