  The charged particle multiplicity ($n_{ch}$) and pseudorapidity density
$(dn_{ch}/d\eta)$ are key observables to characterize the properties of matter
created in heavy ion collisions. The dependence of these observables on
collision energy and the collision geometry are a key tool to understand the
underlying particle production mechanism. Recently a lot of focus has been made
on asymmetric and deformed nuclei collisions since these collisions can provide
a deeper understanding about the nature of quantum chromodynamics (QCD). On
phenomenological perspective a unified model which describes the experimental
data coming from various kind of collision experiments, is much needed to
provide the physical insights about the production mechanism. In this paper, we
have calculated the charged hadron multiplicities for nucleon-nucleus (such as
proton-lead $(p-Pb)$ and asymmetric nuclei collisions like deutron-gold
$(d-Au)$, and copper-gold $(Cu-Au)$ within a new version of wounded quark model
(WQM) and shown their variation with respect to centrality. Further we have
used a suitable density function within our WQM to calculate pseudorapidity
density of charged hadrons at mid-rapidity in the collisions of deformed
uranium nuclei. We found that our model with suitable density functions
describes the experimental data for symmetric, asymmetric and deformed nuclei
collisions simultaneously over a wide range of collision energy.
