  The production of heavy quarkonium as QQbar bound-states in hadron-hadron
collisions is considered within the framework of a space-time description,
combining parton-cascade evolution with a coalescence model for bound-state
formation. The `hard' production of the initial QQbar, directly or via gluon
fragmentation and including both color-singlet and color-octet contributions,
is calculated from the PQCD cross-sections. The subsequent development of the
QQbar system is described within a space-time generalization of the DGLAP
parton-evolution formalism in position- and momentum-space. The actual
formation of the bound-states is accomplished through overlap of the QQbar pair
and a spectrum of quarkonium wave-functions. This coalescence can only occur
after sufficent gluon radiation reduces the QQbar relative velocity to a value
commensurate with the non-relativistic kinematics of these bound systems. The
presence of gluon participants in the cascade then is both necessary and leads
to the natural inclusion of both color-singlet and color-octet mechanisms. The
application of this approach to pp (ppbar) collisions from sqrt(s)= 30 GeV - 14
TeV reveals very decent agreement with available data from ISR and Tevatron -
without the necessity of introducing fit parameters. Moreover, production
probabilities are calculated for a complete spectrum of charmonium and
bottonium states, with the relative significance compared to open charm
(bottom) production. An analysis of the space-time development is carried
through which sheds light on the relevance of gluon radiation and
color-structure, suggesting a correponding experimental investigation.
