The performances of SIW horns antennas diminish significantly when the substrate thickness is much smaller than the free space wavelength lambda(0). Specifically, the mismatch between the antenna aperture and the air yields to unwanted back radiation and poor matching. This paper presents a fully printed structure etched after the horn aperture to simultaneously solve these two problems. Models based on transmission line and array theory have been developed to analyse and synthesize this new type of structure. They provide simple design rules to characterize the SIW horn geometry and to reasonably predict its electromagnetic performances. In addition, the horn profile is further optimized by reducing its dimensions needed for a given directivity. The presented concepts are verified by manufacturing a prototype in a substrate thinner than lambda(0)/10 working between 14.2-15.4 GHz. Its excellent performances (|S-11| < -10 dB and FTBR > 15 dB) together with simple and low-cost construction opens the door to the use of SIW horns in many other applications.