  In color string models, the transverse momentum distribution (TMD) is
obtained through the convolution of the Schwinger mechanism with the string
tension fluctuations distribution. Considering a $q$-Gaussian distribution for
these fluctuations, the TMD becomes a hypergeometric confluent function that
adequately reproduces the characteristic scales at low and high $p_T$ values.
In this approach, the hard scale of the TMD is a consequence of considering a
heavy-tailed distribution for the string tension fluctuations whose width rises
as $\sqrt{s}$, multiplicity or centrality increases. In this paper, we
introduce the complete information of the TMD in the color string percolation
model by means of the determination of the color suppression factor, which now
also depends on the parameters of the $q$-Gaussian. To this end, we analyze the
reported data on pp and AA collisions at different center of mass energies,
multiplicities, and centralities. In particular, for minimum bias pp
collisions, we found that the $q$-Gaussian parameters and the effective
temperature are monotonically increasing functions of the center of mass
energy. Similar results are found for AA collisions as a function of the
centrality at fixed $\sqrt{s}$.
  We summarize these results in a phase diagram that indicates the $q$-Gaussian
parameters region allowing the quark-gluon plasma formation.
