  We develop a new formulation of the quark coalescence model by including the
quark number conservation in order to describe the hadronization of the bulk of
the quark-gluon plasma. The scalings between hadron and quark phase space
distributions are shown to depend on the transverse momentum. For hard quarks,
our general scalings reproduce the usual quadratic scaling relation for mesons
and the cubic scaling relation for baryons. For softer quarks, however, the
inclusion of the quark number conservation leads to a linear scaling for the
hadron species that dominates the quark number of each flavor, while the
scalings of non-dominant hadrons depend on the coalescence dynamics. For charm
mesons, we find that the distribution of soft $D$ mesons does not depend on the
light quark distribution but the distribution of soft $J/\psi$ mesons is
inversely correlated to the light quark distribution.
