  To investigate the origin of the features discovered in the exoplanet
population, the knowledge of exoplanets' mass and radius with a good precision
is essential. In this paper, we report the discovery of three transiting
exoplanets by the SuperWASP survey and the SOPHIE spectrograph with mass and
radius determined with a precision better than 15 %. WASP-151b and WASP-153b
are two hot Saturns with masses, radii, densities and equilibrium temperatures
of 0.31^{+0.04}_{-0.03} MJ, 1.13^{+0.03}_{-0.03} RJ, 0.22^{-0.03}_{-0.02} rhoJ
and 1, 290^{+20}_{-10} K, and 0.39^{+0.02}_{-0.02} MJ, 1.55^{+0.10}_{-0.08} RJ,
0.11^{+0.02}_{-0.02} rhoJ and 1, 700^{+40}_{-40} K, respectively. Their host
stars are early G type stars (with magV ~ 13) and their orbital periods are
4.53 and 3.33 days, respectively. WASP-156b is a Super-Neptune orbiting a K
type star (magV = 11.6) . It has a mass of 0.128^{+0.010}_{-0.009} MJ, a radius
of 0.51^{+0.02}_{-0.02} RJ, a density of 1.0^{+0.1}_{-0.1} rhoJ, an equilibrium
temperature of 970^{+30}_{-20} K and an orbital period of 3.83 days. WASP-151b
is slightly inflated, while WASP-153b presents a significant radius anomaly.
WASP-156b, being one of the few well characterised Super-Neptunes, will help to
constrain the formation of Neptune size planets and the transition between gas
and ice giants. The estimates of the age of these three stars confirms the
tendency for some stars to have gyrochronological ages significantly lower than
their isochronal ages. We propose that high eccentricity migration could
partially explain this behaviour for stars hosting a short period planet.
Finally, these three planets also lie close to (WASP-151b and WASP-153b) or
below (WASP-156b) the upper boundary of the Neptunian desert. Their
characteristics support that the ultra-violet irradiation plays an important
role in this depletion of planets observed in the exoplanet population.
