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Austrian Federal Ministry of Science, Research and Economy ; Austrian Science Fund ; Belgian Fonds de la Recherche Scientifique ; Fonds voor Wetenschappelijk Onderzoek ; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) ; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) ; Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) ; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) ; Bulgarian Ministry of Education and Science ; CERN ; Chinese Academy of Sciences, Ministry of Science and Technology ; National Natural Science Foundation of China ; COLCIENCIAS ; Croatian Ministry of Science, Education and Sport ; Croatian Science Foundation ; Research Promotion Foundation, Cyprus ; Secretariat for Higher Education, Science, Technology and Innovation, Ecuador ; Ministry of Education and Research, Estonian Research Council ; European Regional Development Fund, Estonia ; Academy of Finland, Finnish Ministry of Education and Culture ; Helsinki Institute of Physics ; Institut National de Physique Nucleaire et de Physique des Particules / CNRS ; Commissariat a l'Energie Atomique et aux Energies Alternatives/CEA, France ; Bundesministerium fur Bildung und Forschung ; Deutsche Forschungsgemeinschaft ; Helmholtz-Gemeinschaft Deutscher Forschungszentren, Germany ; General Secretariat for Research and Technology, Greece ; National Scientific Research Foundation ; National Innovation Office, Hungary ; Department of Atomic Energy ; Department of Science and Technology, India ; Institute for Studies in Theoretical Physics and Mathematics, Iran ; Science Foundation, Ireland ; Istituto Nazionale di Fisica Nucleare, Italy ; Ministry of Science, ICT and Future Planning ; National Research Foundation (NRF), Republic of Korea ; Lithuanian Academy of Sciences ; Ministry of Education, and University of Malaya (Malaysia) ; BUAP ; CINVESTAV ; CONACYT ; LNS ; SEP ; UASLP-FAI ; Ministry of Business, Innovation and Employment, New Zealand ; Pakistan Atomic Energy Commission ; Ministry of Science and Higher Education ; National Science Centre, Poland ; Fundacao para a Ciencia e a Tecnologia, Portugal ; JINR, Dubna ; Ministry of Education and Science of the Russian Federation ; Federal Agency of Atomic Energy of the Russian Federation, Russian Academy of Sciences ; Russian Foundation for Basic Research ; Ministry of Education, Science and Technological Development of Serbia ; Secretaria de Estado de Investigacion, Desarrollo e Innovacion and Programa Consolider-Ingenio, Spain ; ETH Board ; ETH Zurich ; PSI ; SNF ; UniZH ; Canton Zurich ; SER ; Ministry of Science and Technology, Taipei ; Thailand Center of Excellence in Physics ; Institute for the Promotion of Teaching Science and Technology of Thailand ; Special Task Force for Activating Research ; National Science and Technology Development Agency of Thailand ; Scientific and Technical Research Council of Turkey ; Turkish Atomic Energy Authority ; National Academy of Sciences of Ukraine ; State Fund for Fundamental Researches, Ukraine ; Science and Technology Facilities Council, UK ; US Department of Energy ; US National Science Foundation ; Marie-Curie programme ; European Research Council ; EPLANET(European Union) ; Leventis Foundation ; A. P. Sloan Foundation ; Alexander von Humboldt Foundation ; Belgian Federal Science Policy Office ; Fonds pour la Formation a la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium) ; Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium) ; Ministry of Education, Youth and Sports (MEYS) of the Czech Republic ; Council of Science and Industrial Research, India ; HOMING PLUS programme of the Foundation for Polish Science ; European Union, Regional Development Fund ; Mobility Plus programme of the Ministry of Science and Higher Education ; National Science Center (Poland) ; Thalis and Aristeia programme ; EU-ESF ; Greek NSRF ; National Priorities Research Program by Qatar National Research Fund ; Programa Clarin-COFUND del Principado de Asturias ; Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University ; Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand) ; Welch Foundation ; Ministry of Education and Research, Estonian Research Council: IUT23-4 ; Ministry of Education and Research, Estonian Research Council: IUT23-6 ; National Science Center (Poland): Harmonia 2014/14/M/ST2/00428 ; National Science Center (Poland): Opus 2013/11/B/ST2/04202 ; National Science Center (Poland): 2014/13/B/ST2/02543 ; National Science Center (Poland): 2014/15/B/ST2/03998 ; National Science Center (Poland): Sonata-bis 2012/07/E/ST2/01406 ; Welch Foundation: C-1845 ; Measurements of the associated production of a Z boson with at least one jet originating from a b quark in proton-proton collisions at root s = 8 TeV are presented. Differential cross sections are measured with data collected by the CMS experiment corresponding to an integrated luminosity of 19.8 fb(-1). Z bosons are reconstructed through their decays to electrons and muons. Cross sections are measured as a function of observables characterizing the kinematics of the b jet and the Z boson. Ratios of differential cross sections for the associated production with at least one b jet to the associated production with any jet are also presented. The production of a Z boson with at least two b jets is investigated, and differential cross sections are measured for the dijet system. Results are compared to theoretical predictions, testing two different flavour schemes for the choice of initial-state partons.