  We study soft hadron production in relativistic heavy ion collisions in a
wide range of reaction energy, 4.8 GeV <sqrt{s_ NN}<200 GeV, and make
predictions about yields of particles using the statistical hadronization
model. In fits to experimental data, we obtain both statistical parameters as
well as physical properties of the hadron source. We identify the properties of
the fireball at the critical energy threshold, 6.26 GeV < sqrt{s_NN}^cr} <7.61
GeV, delineating for higher energies hadronization of an entropy rich phase. In
terms of the chemical composition, one sees a phase which at low energy is
chemically under-saturated, and which turns into a chemically over-saturated
state persisting up to the maximum accessible energy. Assuming that there is no
change in physical mechanisms in the energy range 15>sqrt{s_NN} \ge 200 GeV, we
use continuity of particle yields and statistical parameters to predict the
hadron production at sqrt{s_NN}=62.4 GeV, and obtain total yields of hadrons at
sqrt{s_NN}=130 GeV. We consider, in depth, the pattern we uncover within the
hadronization condition, and discuss possible mechanisms associated with the
identified rapid change in system properties at sqrt{s_NN ^cr}. We propose that
the chemically over-saturated 2+1 flavor hadron matter system undergoes a 1st
order phase transition.
