  We present a detailed study of the Entanglement Entropy for the confining
Klebanov-Strassler background coupled to a large number of dynamical flavors in
the Veneziano limit. As we vary the number of the massless flavors the behavior
of the entropy strongly depends on the way we fix the integration constant of
the warp factor, that is related to the glueball scale. In the case of massive
flavors, the mass of the flavor branes introduces another scale in the
background and the entropy undergoes two first order phase transitions. The
competition between the glueball and the quark scales will lead to a critical
point where one of the phase transitions degenerates to a second order one. We
have calculated the critical exponents and have found that they are independent
of the number of flavors and different from the mean filed theory expectations.
