  A approach of finite size scaling theory for discontinous percolation with
multiple giant clusters is developed in this paper. The percolation in
generalized Bohman-Frieze-Wormald (BFW) model has already been proved to be
discontinuous phase transition. In the evolution process, the size of largest
cluster $s_1$ increases in a stairscase way and its fluctuation shows a series
of peaks corresponding to the jumps of $s_1$ from one stair to another. Several
largest jumps of the size of largest cluster from single edge are studied by
extensive Monte Carlo simulation. $\overline{\Delta}_k(N)$ which is the mean of
the $k$th largest jump of largest cluster, $\overline{r}_k(N)$ which is the
corresponding averaged edge density, $\sigma_{\Delta,k}(N)$ which is the
standard deviation of $\Delta_k$ and $\sigma_{r,k}(N)$ which is the standard
deviation of $r_k$ are analyzed. Rich power law behaviours are found for
$\overline{r}_k(N)$, $\sigma_{\Delta,k}(N)$ and $\sigma_{r,k}(N)$ with critical
exponents denoted as $1/\nu_1$, $(\beta/\nu)_2$ and $1/\nu_2$. Unlike
continuous percolation where the exact critical thresholds and critical
exponent $1/\nu_1$ are used for finite size scaling, the size-dependent pseudo
critical thresholds $\overline{r}_k(N)$ and $1/\nu_2$ works for the data
collapse of the curves of largest cluster and its fluctuation in discontinuous
percolation in BFW model. Further, data collapse can be obtained part by part.
That is, $s_1(r,N)$ can be collapsed for each jump from one stair to another
and its fluctuation can be collapsed around each peak with the corresponding
$\overline{r}_k(N)$ and $1/\nu_2$.
