  The nature of transverse momentum dependence of the inclusive cross-sections
for secondary pions produced in high energy hadronic($PP$), hadronuclear($PA$)
and nuclear($AA$) collisions has here been exhaustively investigated for a
varied range of interactions in a unified way with the help of a master
formula. This formula evolved from a new combination of the basic Hagedorn's
model for particle(pion) production in PP scattering at ISR range of energies,
a phenomenological approach proposed by Peitzmann for converting the results of
$NN(PP)$ reactions to those for either $PA$ or $AA$ collisions, and a specific
form of parametrization for mass number-dependence of the nuclear cross
sections. This grand combination of models(GCM) is then applied to analyse the
assorted extensive data on various high energy collisions. The nature of
qualitative agreement between measurements and calculations on both the
inclusive cross-sections for production of pions, and some ratios of them as
well, is quite satisfactory. The modest successes that we achieve here in
dealing with the massive data-sets are somewhat encouraging in view of the
diversity of the reactions and the very wide range of interaction energies.
