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The periphery of the Small Magellanic Cloud (SMC) can unlock important information regarding galaxy formation and evolution in interacting systems. Here, we present a detailed study of the extended stellar structure of the SMC using deep colour-magnitude diagrams, obtained as part of the Survey of the MAgellanic Stellar History (SMASH). Special care was taken in the decontamination of our data from Milky Way (MW) foreground stars, including from foreground globular clusters NGC 362 and 47 Tuc. We derived the SMC surface brightness using a `conservative' approach from which we calculated the general parameters of the SMC, finding a staggered surface brightness profile. We also traced the fainter outskirts by constructing a stellar density profile. This approach, based on stellar counts of the oldest main-sequence turn-off stars, uncovered a tidally disrupted stellar feature that reaches as far out as 12 deg from the SMC centre. We also serendipitously found a faint feature of unknown origin located at similar to 14 deg from the centre of the SMC and that we tentatively associated with a more distant structure. We compared our results to in-house simulations of a 1 x 10(9) M-circle dot SMC, finding that its elliptical shape can be explained by its tidal disruption under the combined presence of the MW and the Large Magellanic Cloud. Finally, we found that the older stellar populations show a smooth profile while the younger component presents a jump in the density followed by a flat profile, confirming the heavily disturbed nature of the SMC. © 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society ; SRM acknowledges funding from grant AST-1909497 from the National Science Foundation. AM acknowledges support from Fondo Nacional de Desarrollo Cientifico y Tecnologico (FONDECYT) Regular grant 1181797 and funding from the Max Planck Society through a Partner Group grant. NFM gratefully acknowledge support from the French National Research Agency (ANR) funded project 'Pristine' (ANR-18-CE31-0017) along with funding from INSU,CNRS through the Programme National Galaxies et Cosmologie. M-RC and CPMB acknowledge support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 682115). RRM acknowledges partial support from project BASAL AFB-170002 as well as FONDECYT project N. 1170364. CG, TRL, and MMacknowledge financial support through the grants (AEI/FEDER, UE) AYA2017-89076-P and AYA2015-63810-P, as well as by the Ministerio de Ciencia, Innovacion y Universidades (MCIU), through the State Budget and by the Consejeria de Economia, Industria, Comercio y Conocimiento of the Canary Islands Autonomous Community, through the Regional Budget (including IAC project, TRACES). TRL is also supported by grant AYA2016-77237-C3-1-P (RAVET project) and a MCIU Juan de la Cierva - Formacion grant (FJCI-2016-30342). DMDacknowledges financial support from the State Agency for Research of the Spanish MCIU through the 'Centre of Excellence Severo Ochoa' award for the Instituto de Astrof ' isica de Andalucia (SEV-2017-0709). Based on observations at Cerro Tololo Inter-American Observatory, NSF's National Optical-Infrared Astronomy Research Laboratory (NOIRLab Prop. ID: 2013A-0411 and 2013B-0440; PI: Nidever), which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. This project used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaborating institutions: Argonne National Lab, University of California Santa Cruz, University of Cambridge, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, University of Chicago, University College London, DES-Brazil consortium, University of Edinburgh, ETH-Zurich, University of Illinois at Urbana-Champaign, Institut de Ci`encies de l'Espai, Institut de F ' isica d'Altes Energies, Lawrence Berkeley National Lab, Ludwig-Maximilians Universitat, University of Michigan, National Optical Astronomy Observatory, University of Nottingham, Ohio State University, University of Pennsylvania, University of Portsmouth, SLAC National Lab, Stanford University, University of Sussex, and Texas A&M University. Funding for DES, including DECam, has been provided by the U.S. Department of Energy, National Science Foundation, Ministry of Education and Science (Spain), Science and Technology Facilities Council (UK), Higher Education Funding Council for England (England), National Center for Supercomputing Applications, Kavli Institute for Cosmological Physics, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo a Pesquisa, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and the Ministerio da Ciencia e Tecnologia (Brazil), the German Research Foundation-sponsored cluster of excellence `Origin and Structure of the Universe' and the DES collaborating institutions. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. ; Peer reviewed