This paper is part of a series of publications concerning the development of the European DEMO during the pre- conceptual design phase (2014-2020). In particular, it deals with the physics basis employed for the definition of the various DEMO baselines released, and the assumptions adopted where necessary. In the course of the pre-conceptual design phase, some of these assumptions have been progressively replaced with results of dedicated modelling activities or code developments in general, which are summarized here. The considered baselines, obtained with the systems code PROCESS, are the EU-DEMO 2015, 2017 and 2018, based on an ITER-like ELMy H-mode confinement regime. In addition, a QH-mode baseline and an I-mode baseline have been produced in 2019, and are analysed here in detail as well. Furthermore, a discussion on the main knowledge gaps, as well as the strategy to be adopted in the next phases to close them, relying on the contribution of the European and international fusion research, is provided.