  We establish the updated version of dynamical core--corona initialization
framework (DCCI2) as a unified description from small to large colliding
systems and from low to high transverse momentum ($p_T$) regions. Using DCCI2,
we investigate effects of interplay between locally equilibrated and
non-equilibrated systems, in other words, core and corona components in
high-energy nuclear collisions. Given experimental multiplicity distributions
and yield ratios of $\Omega$ baryons to charged pions as inputs, we extract the
fraction of core and corona components in p+p collisions at $\sqrt{s}=7$ TeV
and Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. We find core contribution
overtakes corona contribution as increasing multiplicity above $\langle
dN_{\mathrm{ch}}/d\eta \rangle_{|\eta|<0.5} \sim 18$ regardless of the
collision system or energy. We also see that the core contribution exceeds the
corona contribution only in 0.0-0.95\% multiplicity class in p+p collisions.
Notably, there is a small enhancement of corona contribution with $\sim20$\%
below $p_T\sim 1$ GeV even in minimum bias Pb+Pb collisions. We find that the
corona contribution at low $p_T$ gives $\sim 15$-$38$ $\%$ correction on
$v_2\{2\}$ at $N_{\mathrm{ch}}\lesssim 370$. This raises a problem in
conventional hydrodynamic analyses in which low $p_T$ soft hadrons originate
solely from core components. We finally scrutinize the roles of string
fragmentation and the longitudinal expansion in the transverse energy per unit
rapidity, which is crucial in initial conditions for hydrodynamics from event
generators based on string models.
