  Two aspects of high-energy \pp collisions share common phenomenological
elements: (a) A correlation between jet production and \pp centrality is
suggested by the transverse partonic structure of hadrons inferred from
deep-inelastic scattering data. (b) The {\em underlying event} (UE) is defined
as the final-state particles complementary to a triggered high-energy dijet. An
observable common to both topics is variation of so-called {\em transverse
multiplicity} $N_\perp$ with a $p_{t,trig}$ dijet trigger. We test assumptions
associated with \pp collision centrality and the UE. We determine the nature of
the UE and explore the relation between jet production and \pp centrality. We
use the {\em two-component model} (TCM) of spectra and correlations derived
from 200 GeV \pp collisions to construct a simulated particle distribution on
$(p_t,n_{ch})$ to predict the $N_\perp$ response to $p_{t,trig}$. The $p_t$
spectrum TCM combined in this analysis with measured minimum-bias \pp angular
correlations suggests that the UE includes a substantial contribution from the
triggered dijet in addition to the contribution from projectile fragmentation
(beam-beam remnants). The jet contribution to $N_\perp$ may represent a
universal large-angle base common to all dijets that extends across $2\pi$
azimuth. The analysis further suggests that \pp centrality is not controlled
significantly by $p_{t,trig}$ but may be correlated to some extent with an
imposed $n_{ch}$ condition, depending on the role of fluctuations. Future
correlation studies may better determine the role of \pp centrality. These
results may have implications for ongoing RHIC analysis and LHC searches for
physics beyond the standard model.
