We report measurements of the primary

charged particle pseudorapidity density and transverse momentum

distributions in p-Pb collisions at sqrt(s_nn) = 5.02 TeV, and

investigate their correlation with experimental observables sensitive

to the centrality of the collision. Centrality classes are defined

using cuts on different event activity estimators, i.e. charged

particle multiplicities measured in three disjunct pseudorapidity

regions as well as the energy measured at beam rapidity (zero-degree).

The procedures to determine the centrality, quantified by the number

of participants (Npart), or the number of nucleon-nucleon binary

collisions (Ncoll), are described. We show that, in contrast

to Pb-Pb collisions, in p-Pb collisions large multiplicity

fluctuations together with the small range of participants available,

generate a dynamical bias in centrality classes based on particle

multiplicity. As an alternative event-centrality estimator, we

propose to use the zero-degree energy, which we expect does not

induce any dynamical bias. Based on zero-degree energy

centrality classes, the \Npart\ dependence of particle production is

studied. Under the assumption that the multiplicity measured in the

Pb-going rapidity region scales with the number of Pb-participants, an

approximate independence of the multiplicity per participating nucleon

measured at mid-rapitity of the number of participating nucleons is

observed. Furthermore, at high-pt the p-Pb spectra are found to be

consistent with the pp spectra scaled by Ncoll for all centrality

classes. Our results are expected to put constraints on the

description of particle production in high-energy heavy-ion collisions.