  In the frame work of a nuclear overlap model, we estimate the number of
nucleon and quark participants in proton-proton, proton-nucleus and
nucleus-nucleus collisions. We observe the number of nucleon
($N_{N-part}$)-normalized enhancement of multi-strange particles which show a
monotonic increase with centrality, turns out to be a centrality independent
scaling behavior when normalized to number of constituent quarks participating
in the collision ($N_{q-part}$). In addition, we observe that the
$N_{q-part}$-normalized enhancement, when further normalized to the strangeness
content, shows a strangeness independent scaling behavior. This holds good at
top RHIC energy. However, the corresponding SPS data show a weak
$N_{q-part}$-scaling with strangeness scaling being violated at top SPS energy.
This scaling at RHIC indicates that the partonic degrees of freedom playing an
important role in the production of multi-strange particles. Top SPS energy, in
view of the above observations, shows a co-existence of hadronic and partonic
phases. We give a comparison of data with HIJING, AMPT and UrQMD models to
understand the particle production dynamics at different energies.
