Résumé : The almost hermetic coverage of the CMS detector is used to measure the distribution of transverse energy, Eτ, over 13.2 units of pseudorapidity η for pPb collisions at a center-of-mass energy per nucleon pair of √sNN=5.02 TeV. 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-goingbeam directions. This wide acceptance enables the study of correlations between well-separated angular regionsand makes the measurement a particularly powerful test of event generators. For minimum biaspPb collisionsthe maximum value of dEτ/dη is 22 GeV, which implies an Eτ per participant nucleon pair comparable to thatof peripheral PbPb collisions at √sNN=2.76 TeV. The increase of dEτ/dη with centrality is much stronger forthe lead-going side than for the proton-going side. The η dependence of dEτ/dη is sensitive to the η range inwhich the centrality variable is defined. Several modern generators are compared to these results but none isable to capture all aspects of the η and centrality dependence of the data and the correlations observed between different η regions.