The use of multiple integral field units with FLAMES/GIRAFFE at VLT has revolutionized investigations of distant galaxy kinematics. This facility may recover the velocity fields of almost all emission line galaxies with I_(AB)<22.5 at z<0.8. We have gathered a unique sample of 63 velocity fields at z=0.4-0.75, which are representative of M_stellar > 1.5*10^10 M_sun emission line W_0([OII])>15 AA galaxies, and are unaffected by cosmic variance. Taking into account all galaxies -with or without emission lines- in that redshift range, we find that 42+/-7% of them have anomalous kinematics, including 26+/-7% with complex kinematics, i.e. not supported by either rotation or by dispersion. The large fraction of complex velocity fields suggests a large impact of merging in shaping the galaxies in the intermediate mass range. We discuss how this can be accommodated within the frame of current scenarios of galaxy formation, including for the Milky Way and M31.