  Small planets ($\sim$1--3.9 $\Rearth$) constitute more than half of the
inventory of the 4000-plus exoplanets discovered so far. Smaller planets are
sufficiently dense to be rocky, but those with radii larger than $\sim$1.6
$\Rearth$ are thought to display in many cases hydrogen/helium gaseous
envelopes up to $\sim$30\% of the planetary mass. These low-mass planets are
highly irradiated and the question of their origin, evolution, and possible
links remains open. Here we show that close-in ocean planets affected by
greenhouse effect display hydrospheres in supercritical state, which generate
inflated atmospheres without invoking the presence of large hydrogen/helium
gaseous envelopes. We present a new set of mass-radius relationships for ocean
planets with different compositions and different equilibrium temperatures,
which are found to be well adapted to low-density sub-Neptune planets. Our
model suggests that super-Earths and water-rich sub-Neptunes could belong to
the same family of planets, i.e. hydrogen/helium-free planets, with differences
between their interiors simply resulting from the variation in the water
content.
