The properties of the propagation and of the absorption of electron cyclotron extraordinary waves injected obliquely with respect to the external magnetic field in the meridian plane of a Tokamak-like plasma slab are studied by means of a system of wave-dynamical, hot and weakly relativistic propagation equations. The boundary value problem associated to this system is solved in a global way, thereby permitting the analysis of mode conversion between the incident extraordinary wave and the electron Bernstein wave. The results of rather wide scanning in density, electron temperature and injection angle are presented. In the low density regime the total absorption increases with the obliquity of the launch, according to the WKB theory. In the high density regime, well above the cold high-density cut-off, an unexpected absorption is found for small values of the angle of injection, respect to the direction of the magnetic field. This absorption is appreciable even for moderately high values of the electron temperature.