  Measurements of event-ensemble mean transverse momentum $\langle p_t \rangle$
vs charged-hadron multiplicity $n_{ch}$ for $p_t$ spectra from 5 TeV p-Pb and
2.76 TeV Pb-Pb collisions and from p-p collisions for several energies have
been reported recently. While in all cases $\langle p_t \rangle$ increases
monotonically with $n_{ch}$ the rate of increase is very different from system
to system. Comparisons with several theory Monte Carlos reveal substantial
disagreements and lead to considerable uncertainty on how to interpret the
$\langle p_t \rangle$ data. In the present study we develop a two-component
(soft+hard) model (TCM) of $p_t$ production in high energy nuclear collisions
and apply it to the $\langle p_t \rangle$ data. The soft component is assumed
to be a universal feature of high energy collisions independent of A-B system
or energy. The hard-component model is based on the observation that dijet
production in p-p collisions does not satisfy the eikonal approximation but
does so in A-A collisions. Hard-component properties are determined from
previous measurements of hadron spectrum hard components, jet spectra and
fragmentation functions. The TCM describes the p-p and Pb-Pb $\langle p_t
\rangle$ data accurately, within data uncertainties, and the p-Pb data appear
to transition smoothly from p-p to A-A $n_{ch}$ trends.
