  In string percolation model, the study of colliding systems at high energies
is based on a continuum percolation theory in two dimensions where the number
of strings distributed in the surface of interest is strongly determined by the
size and the energy of the colliding particles. It is also expected that the
surface where the disks are lying be finite, defining a system without periodic
boundary conditions. In this work, we report modifications to the fraction of
the area covered by disks in continuum percolating systems due to a finite
number of disks and bounded by different geometries: circle, ellipse, triangle,
square and pentagon, which correspond to the first Fourier modes of the shape
fluctuation of the initial state after the particle collision. We find that the
deviation of the fraction of area covered by disks from its corresponding value
in the thermodynamic limit satisfies a universal behavior, where the free
parameters depend on the density profile, number of disks and the shape of the
boundary. Consequently, it is also found that the color suppression factor of
the string percolation model is modified by a damping function related to the
small-bounded effects. Corrections to the temperature and the speed of sound
defined in string systems are also shown for small and elliptically bounded
systems.
