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The catalogue are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/647/A89 Context. The morphology of galaxies provide us with a unique tool for relating and understanding other physical properties and their changes over the course of cosmic time. It is only recently that we have been afforded access to a wealth of data for an unprecedented number galaxies thanks to large and deep surveys. Aims. We present the morphological catalogue of the OTELO survey galaxies detected with the Hubble Space Telescope (HST)-ACS F814W images. We explore various methods applied in previous works to separate early-type (ET) and late-type (LT) galaxies classified via spectral energy distribution (SED) fittings using galaxy templates. Together with this article, we are releasing a catalogue containing the main morphological parameters in the F606W and F814W bands derived for more than 8000 sources. Methods. The morphological analysis is based on the single-Sérsic profile fit. We used the GALAPAGOS2 software to provide multi-wavelength morphological parameters fitted simultaneously in two HST-ACS bands. The GALAPAGOS2 software detects, prepares guess values for GALFIT-M, and provides the best-fitting single-Sérsic model in both bands for each source. Stellar masses were estimated using synthetic rest-frame magnitudes recovered from SED fittings of galaxy templates. The morphological catalogue is complemented with concentration indexes from a separate SExtractor dual, high dynamical range mode. Results. A total of 8812 sources were successfully fitted with single-Sérsic profiles. The analysis of a carefully selected sample of ∼3000 sources up to zphot = 2 is presented in this work, of which 873 sources were not detected in previous studies. We found no statistical evidence for the evolution of the low-mass end of mass–size relation for ET and LT since z = 2. Furthermore, we found a good agreement for the median size evolution for ET and LT galaxies, for a given stellar mass, with the data from the literature. Compared to previous works on faint field galaxies, we found similarities regarding their rest-frame colours as well as the Sérsic and concentration indices. This work was supported by the project Evolution of Galaxies, of reference AYA2014-58861-C3-1-P and AYA2017-88007-C3-1-P, within the "Programa estatal de fomento de la investigacion cientifica y tecnica de excelencia del Plan Estatal de Investigacion Cientifica y Tecnica y de Innovacion (2013-2016)" of the "Agencia Estatal de Investigacion del Ministerio de Ciencia, Innovacion y Universidades", and co-financed by the FEDER "Fondo Europeo de Desarrollo Regional". APG, RPM and MSP was supported by AYA2017-88007-C3-2-P. APG and MC are also supported by the Spanish State Research Agency grant MDM-2017-0737 (Unidad de Excelencia Maria de Maeztu CAB). JAD is grateful for the support from the UNAM-DGAPA-PASPA 2019 program, and the kind hospitality of the IAC. Based on observations made with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias, on the island of La Palma. This paper made use of the IAC Supercomputing facility HTCondor (http://research.cs.wisc.edu/htcondor/). This paper made use of the Wright (2006) cosmological calculator. Based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/IRFU, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Science de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at Terapix available at the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. M.A.L.L. is a DARK-Carlsberg Foundation Fellow (Semper Ardens project CF15-0384). MP acknowledges financial financial support from the Ethiopian Space Science and Technology Institute (ESSTI) under the Ethiopian Ministry of Innovation and Technology (MInT), and of the Spanish MEC undergrant AYA2016-76682-C3-1-P and PID2019-106027GB-C41 and financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofisica de Andaluca (SEV-2017-0709). Peerreview