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We address the 'plane of satellites problem' by studying planar configurations around two disc galaxies with no late major mergers, formed in zoom-in hydro-simulations. Due to the current lack of good quality kinematic data for M31 satellites, we use only positional information. So far, positional analyses of simulations are unable to find planes as thin and populated as the observed ones. Moreover, they miss systematicity and detail in the plane-searching techniques, as well as in the study of the properties and quality of planes, both in simulations or real data. To fill this gap, i) we extend the 4-galaxy-normal density plot method (Pawlowski et al. 2013) in a way designed to efficiently identify the best quality planes (i.e., thin and populated) without imposing extra constraints on their properties, and ii), we apply it for the first time to simulations. Using zoom-in simulations allows us to mimic MW/M31-like systems regarding the number of satellites involved as well as the galactic disc mass and morphology, in view of possible disc effects. At all timesteps analyzed in both simulations we find satellite planar configurations that are compatible, along given time intervals, with all the spatial characteristics of observed planes identified using the same methodology. However, the fraction of co-orbiting satellites within them is in general low, suggesting time-varying satellite membership. We conclude that high-quality positional planes of satellites are not infrequent in LCDM-formed disc galaxies with a quiet assembly history. Detecting kinematically-coherent, time-persistent planes demands considering the full six-dimensional phase-space information of satellites.