  We report studies of charge-independent (CI) and charge-dependent (CD)
two-particle differential number correlation functions, $R_{2} \left( \Delta
\eta, \Delta \varphi \right)$, and transverse momentum correlation functions,
$P_2 \left( \Delta \eta, \Delta \varphi \right)$ of charged particles produced
in \PbPb\ collisions at the LHC centre-of-mass energy $\sqrt{s_{\rm NN}} =$
2.76 TeV with the UrQMD, AMPT and EPOS models. Model predictions for $R_2$ and
$P_2$ correlation functions are presented for inclusive charged hadrons
($h^\pm$) in selected transverse momentum ranges and with full azimuthal
coverage in the pseudorapidity range $|\eta|< 1.0$. We compare these
predictions for the strength, shape, and particularly the width of the
correlation functions with recent measurements of these observables by the
ALICE collaboration. Our analysis indicate that comparative studies of $R_2$
and $P_2$ correlation functions provide valuable insight towards the
understanding of particle production in Pb--Pb collisions. We find, in
particular, that these models have quantitatively different predictions for
these three observables but none reproduce the measured correlation functions
reported by the ALICE collaboration. Accounting for quantum number conservation
in models, particularly charge conservation, is mandatory to reproduce the
detailed measurements of number and transverse momentum correlation functions.
