In a simplified model we study the hadronization of quark matter in an expa
nding fireball, in particular the approach to a final hadronic composition
in equilibrium. Ideal hadron gas equilibrium constrained by conservation la
ws, the fugacity parametrization, as well as linear and nonlinear coalescen
ce approaches are recognized as different approximations to this in-medium
quark fusion process. It is shown that colour confinement requires a depend
ence of the hadronization cross section on quark density in the presence of
flow (dynamical confinement).