  We test the universal finite-size scaling of the cluster mass order parameter
in two-dimensional (2D) isotropic and directed continuum percolation models
below the percolation threshold by computer simulations. We found that the
simulation data in the 2D continuum models obey the same scaling expression of
mass M to sample size L as generally accepted for isotropic lattice problems,
but with a positive sign of the slope in the ln-ln plot of M versus L. Another
interesting aspect of the finite-size 2D models is also suggested by plotting
the normalized mass in 2D continuum and lattice bond percolation models, versus
an effective percolation parameter, independently of the system structure (i.e.
lattice or continuum) and of the possible directions allowed for percolation
(i.e. isotropic or directed) in regions close to the percolation thresholds.
Our study is the first attempt to map the scaling behaviour of the mass for
both lattice and continuum model systems into one curve.
