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Aims. We study the possible atmospheric mass loss from 57 known transiting exoplanets around F, G, K, and M-type stars over evolutionary timescales. For stellar wind induced mass loss studies, we estimate the position of the pressure balance boundary between Coronal Mass Ejection (CME) and stellar wind ram pressures and the planetary ionosphere pressure for non- or weakly magnetized gas giants at close orbits. Methods. The thermal mass loss of atomic hydrogen is calculated by a mass loss equation where we consider a realistic heating e ciency, a radius-scaling law and a mass loss enhancement factor due to stellar tidal forces. The model takes into account the temporal evolution of the stellar EUV flux by applying power laws for F, G, K, and M-type stars. The planetary ionopause obstacle, which is an important factor for ion pick-up escape from non- or weakly magnetized gas giants is estimated by applying empirical power-laws. Results. By assuming a realistic heating e ciency of about 10-25% we found that WASP-12b may have lost about 6-12% of its mass during its lifetime. A few transiting low density gas giants at similar orbital location, like WASP-13b, WASP-15b, CoRoT-1b or CoRoT-5b may have lost up to 1-4% of their initial mass. All other transiting exoplanets in our sample experience negligible thermal loss ( 1%) during their lifetime. We found that the ionospheric pressure can balance the impinging dense stellar wind and average CME plasma flows at distances which are above the visual radius of "Hot Jupiters", resulting in mass losses < 2% over evolutionary timescales. The ram pressure of fast CMEs cannot be balanced by the ionospheric plasma pressure for orbital distances between 0.02-0.1 AU. Therefore, collisions of fast CMEs with hot gas giants should result in large atmospheric losses which may influence the mass evolution of gas giants with masses < MJup. Depending on the stellar luminosity spectral type, planetary density, heating e ciency, orbital distance, and the related Roche lobe e ect, we expect that at distances between 0.015-0.02 AU, Jupiter-class and sub-Jupiter-class exoplanets can lose several percent of their initial mass. At orbital distances 0:015 AU, low density hot gas giants in orbits around solar type stars may even evaporate down to their coresize, while low density Neptune-class objects can lose their hydrogen envelopes at orbital distances 0:02 AU.

Determining the mass loss limit for close-in exoplanets: what can we learn from transit observations?