During the first billion years of their life, exoplanet atmospheres are modified by different atmospheric escape phenomena that can strongly affect the shape and morphology of the exoplanet itself. These processes can be studied with Lyα, Hα, and/or He I triplet observations. We present high-resolution spectroscopy observations from CARMENES and GIARPS checking for He I and Hα signals in 20 exoplanetary atmospheres: V1298 Tau c, K2-100 b, HD 63433 b, HD 63433 c, HD 73583 b, HD 73583 c, K2-77 b, TOI-2076 b, TOI-2048 b, HD 235088 b, TOI-1807 b, TOI-1136 d, TOI-1268 b, TOI-1683 b, TOI-2018 b, MASCARA-2b, WASP-189 b, TOI-2046 b, TOI-1431 b, and HAT-P-57 b. We report two new high-resolution spectroscopy He I detections for TOI-1268 b and TOI-2018 b, and a Hα detection for TOI-1136 d. Furthermore, we detect hints of He I for HD 63433 b, and Hα for HD 73583 b and c, which need to be confirmed. The aim of the Measuring Out-flows in Planets orbiting Young Stars (MOPYS) project is to understand the evaporating phenomena and test their predictions from the current observations. We compiled a list of 70 exoplanets with He I and/or Hα observations, from this work and the literature, and we considered the He I and Hα results as proxy for atmospheric escape. Our principal results are that 0.1–1 Gyr planets do not exhibit more He I or Hα detections than older planets, and evaporation signals are more frequent for planets orbiting ~1–3 Gyr stars. We provide new constraints to the cosmic shoreline, the empirical division between rocky planets and planets with atmosphere, by using the evaporation detections and we explore the capabilities of a new dimensionless parameter, RHe/RHill, to explain the He I triplet detections. Furthermore, we present a statistically significant upper boundary for the He I triplet detections in the Teq versus ρp parameter space. Planets located above that boundary are unlikely to show He I absorption signals.