The almost hermetic coverage of the CMS detector is used to measure the distribution of transverse energy, ET, over 13.2 units of pseudorapidity, η, for pPb collisions at a center-of-mass energy per nucleon pair of √sNN=5.02TeV. The huge angular acceptance exploits the fact that the CASTOR calorimeter at −6.6<η<−5.2 is effectively present on both sides of the colliding system because of a switch in the proton-going and lead-going beam directions. This wide acceptance enables the study of correlations between well-separated angular regions and makes the measurement a particularly powerful test of event generators. For minimum bias pPb collisions the maximum value of dET/dη is 22GeV, which implies an ET per participant nucleon pair comparable to that of peripheral PbPb collisions at √sNN=2.76TeV. The increase of dET/dη with centrality is much stronger for the lead-going side than for the proton-going side. The η dependence of dET/dη is sensitive to the η range in which the centrality variable is defined. Several modern generators are compared to these results but none is able to capture all aspects of the η and centrality dependence of the data and the correlations observed between different η regions.Received 12 October 2018DOI:https://doi.org/10.1103/PhysRevC.100.024902Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.©2019 CERN, for the CMS CollaborationPhysics Subject Headings (PhySH)Nucleon induced nuclear reactionsResearch AreasNuclear reactionsNucleon induced nuclear reactionsResearch AreasNucleon induced nuclear reactionsParticle correlations & fluctuationsRelativistic heavy-ion collisionsTechniquesHadron collidersNuclear PhysicsParticles & Fields