  Percolation models with multiple percolating clusters have attracted much
attention in recent years. Here we use Monte Carlo simulations to study bond
percolation on $L_{1}\times L_{2}$ planar random lattices, duals of random
lattices, and square lattices with free and periodic boundary conditions, in
vertical and horizontal directions, respectively, and with various aspect ratio
$L_{1}/L_{2}$. We calculate the probability for the appearance of $n$
percolating clusters, $W_{n},$ the percolating probabilities, $P$, the average
fraction of lattice bonds (sites) in the percolating clusters, $<c^{b}>_{n}$
($<c^{s}>_{n}$), and the probability distribution function for the fraction $c$
of lattice bonds (sites), in percolating clusters of subgraphs with $n$
percolating clusters, $f_{n}(c^{b})$ ($f_{n}(c^{s})$). Using a small number of
nonuniversal metric factors, we find that $W_{n}$, $P$, $<c^{b}>_{n}$
($<c^{s}>_{n}$), and $f_{n}(c^{b})$ ($f_{n}(c^{s})$) for random lattices, duals
of random lattices, and square lattices have the same universal finite-size
scaling functions. We also find that nonuniversal metric factors are
independent of boundary conditions and aspect ratios.
