We will show the results of two large parametric climate state studies for tidally locked terrestrial planets around M dwarf stars. We investigated for an Earth-like atmosphere and thermal forcing, 3D climate states for rocky planets with sizes between 1-2 Earth radii, orbital periods between 1-100 days, and also for different surface friction scenarios. We identified distinct climate state transitions that occur for faster and faster orbital periods, that is, towards the inner edge of the habitable zone. In addition, two regions of climate state degeneracies were found. The different climate states - in particular at the inner edge of the habitable zone - show large differences in surface temperatures, circulation and wind systems. Furthermore, different climate states are favoured in our model for different planet sizes and for different surface friction efficiencies. Our studies provide the first "map" for the 3D circulation system to be expected on tidally locked rocky planets around M dwarfs. They will help to better identify potentially habitable planets with relative short orbital periods.