  It has been shown that a hot and dense deconfined nuclear matter state
produced in ultra-relativistic heavy-ion collisions, can be quantitatively
described by the String Percolation phenomenological model. The model address
the phase transition in terms of the two-dimensional continuum percolation
theory over strings, which are schematic representations of the fundamental
interactions among the partons of the colliding nuclei in the initial state. In
this work, we present an extension of the critical string density results
including the eccentricity dependence on the initial state geometry focus on
small string number with different density profile, small deviations from the
different profile densities are found. The percolation threshold shows
consistency with the thermodynamic limit for the uniform density profile with a
large number of strings in the case of circular boundary system. A significant
dependence on the eccentricity for a small number of strings compared to high
occupancy systems is exhibited, the implications may become relevant in
hadron-hadron or hadron-nucleus collision systems.
