We study the formation of early-type galaxies through mergers with a sample of 70 high-resolution (softening length < 60 pc and 12*10^6 particles) numerical simulations of binary mergers of disc galaxies and 16 simulations of ETG remergers. These simulations, designed to accompany observations and models conducted within the Atlas3D project, encompass various mass ratios (from 1:1 to 6:1), initial conditions and orbital parameters. The progenitor disc galaxies are spiral-like with bulge to disc ratios typical of Sb and Sc galaxies. We find that binary mergers of disc galaxies with mass ratios of 3:1 and 6:1 are nearly always classified as Fast Rotators according to the Atlas3D criterion (based on the lambda_R parameter): they preserve the structure of the input fast rotating spiral progenitors. They have intrinsic ellipticities larger than 0.5, cover intrinsic lambda_R values between 0.2 and 0.6, within the range of observed Fast Rotators. Major disc mergers (mass ratios of 2:1 and 1:1) lead to both Fast and Slow Rotators. Most of the Fast Rotators produced in major mergers have intermediate flattening, with ellipticities between 0.4 and 0.6. Most Slow Rotators formed in these binary disc mergers hold a stellar Kinematically Distinct Core (KDC) in their 1-3 central kilo-parsec: these KDCs are built from the stellar components of the progenitors. Besides a handful of specific observed systems -- the counter-rotating discs (2-sigma galaxies) -- these therefore cannot reproduce the observed population of Slow Rotators in the nearby Universe. The mass ratio of the progenitors is a fundamental parameter for the formation of Slow Rotators in these binary mergers, but it also requires a retrograde spin for the earlier-type (Sb) progenitor galaxy with respect to the orbital angular momentum. (Abridged)
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