  On the basis of exactly solvable models with the tricritical and critical
endpoints I discuss the physical mechanism of endpoints formation which is
similar to the usual liquids. It is demonstrated that the necessary condition
for the transformation of the 1-st order deconfinement phase transition into
the 2-nd order phase transition at the (tri)critical endpoint is the vanishing
of surface tension coefficient of large/heavy QGP bags. Using the novel model
of the confinement phenomenon I argue that the physical reason for the
cross-over appearance at low baryonic densities is the negative value of QGP
bag surface tension coefficient. This implies the existence of highly
non-spherical or, probably, even fractal surfaces of large and heavy bags at
and above the cross-over, which, perhaps, can be observed via some
correlations. The model with the tricritical endpoint predicts that at the
deconfinement transition line the volume (mass) distribution of large (heavy)
QGP bags acquires the power law form at the endpoint only, while in the model
with the critical endpoint such a power law exists inside the mixed phase. The
role of finite width of QGP bags is also discussed.
