  A recent study of 5 TeV $p$-Pb centrality combined a Glauber model of $p$-Pb
collision geometry with an assumption of linear scaling between $n_{ch}$
(charge) integrated within some $\eta$ acceptance and the number of nucleon
participants $N_{part}$. The study concluded that $N_{part}$ increases to
nearly 16 in central collisions, and the high-$p_t$ region of $p$-Pb $p_t$
spectra rescaled by the Glauber-estimated number of $p$-N binary collisions
remains consistent with a $p$-$p$ spectrum for the same energy, independent of
$p$-Pb centrality. However, the relation between $N_{part}$ and $n_{ch}$
derived from a two-component (soft + hard) model (TCM) study of ensemble-mean
$\bar p_t$ data for the same system is quite different. This article reports a
detailed analysis of the Glauber study and the question of centrality in $p$-A
collisions. The Glauber centrality model is compared with the $\bar p_t$ TCM to
understand the sources of major differences. The assumption of linear
proportionality between $n_{ch}$ and $N_{part}$ is found to be inconsistent
with $\bar p_t$ data. Properties of the convolution integral relating a
differential cross section and hadron production model to an event distribution
on $n_{ch}$ are examined. An alternative differential-cross-section
distribution is inferred from charge-multiplicity data, and the upper limit on
$N_{part}$ is estimated to be near 8. The TCM centrality model is then applied
to $p_t$ spectrum ratios to predict results for $p$-Pb spectra. The spectrum
TCM is tested with identified-pion spectra from 5 TeV $p$-Pb collisions and the
result is consistent with previous $p$-$p$ TCM results. A TCM prediction that
the spectrum ratio at high $p_t$ should increase to 14 for central $p$-Pb
collisions due to quadratic dependence of dijet production on $n_{ch}$ is
consistent with $\bar p_t$ data from the same system.
