  Multiplicity and pseudorapidity ($\eta$) density ($dN_{\rm ch}/d\eta$)
distributions of charged hadrons provide key information towards understanding
the particle production mechanisms and initial conditions of high-energy
heavy-ion collisions. However, detector constraints limit the $\eta$-range
across which charged particle measurements can be carried out. Extrapolating
the measured distributions to large $\eta$-range by parameterizing measured
distributions and by using calculations from event generators, we characterize
the production of charged particles over the full kinematic range. In the
present study, we use three different ans$\ddot{\mathrm a}$tze to obtain
quantitative descriptions of the shape of pseudorapidity distributions of
charged hadrons produced in pp, p-A, and A-A collisions for beam energies
($\sqrt{s_{\rm NN}}$) ranging from a few GeV to a few TeV corresponding to RHIC
and LHC energies. We study the limiting fragmentation behavior in these
collisions and report evidence for participant-scaling violations in
high-energy collisions at the TeV scale. We additionally examine measured
pseudorapidity distributions to constrain models describing initial conditions
of particle production. We predict the centrality dependence of charged
particle multiplicity distributions at FAIR and NICA energies and give an
estimation of charged particle multiplicity at $\eta=0$ for the proposed HE-LHC
and FCC energies.
