  The radius valley separating super-Earths from mini-Neptunes is a fundamental
benchmark for theories of planet formation and evolution. Observations show
that the location of the radius valley decreases with decreasing stellar mass
and with increasing orbital period. Here, we build from our previous
pebble-based formation model, which, combined with photoevaporation after disc
dispersal, unveiled the radius valley as a separator between rocky- and
water-worlds. We expand our models for a range of stellar masses spanning from
0.1 to 1.5 $M_\odot$. We find that the location of the radius valley is well
described by a power-law in stellar mass as $R_{\rm valley} = 1.8197 \,
M_{\star}^{\!0.14({+0.02}/{-0.01})}$, which is in excellent agreement with
observations. We also find very good agreement with the dependence of the
radius valley on orbital period, both for FGK- and M-dwarfs. Additionally, we
note that the radius valley gets filled towards low stellar masses,
particularly at 0.1-0.4 $M_\odot$, yielding a rather flat slope in $R_{\rm
valley} - P_{\rm orb}$. This is the result of orbital migration occurring at
lower planet mass for less massive stars, which allows for low-mass
water-worlds to reach the inner regions of the system, blurring the separation
in mass (and size) between rocky- and water-worlds. Furthermore, we find that
for planetary equilibrium temperatures above 400 K, the water in the volatile
layer exists fully in the form of steam, puffing the planet radius up compared
to condensed-water worlds. This produces an increase in planet radii of $\sim
30\%$ at 1 $M_\oplus$, and of $\sim 15\%$ at 5 $M_\oplus$, compared to
condensed-water-worlds. As with Sun-like stars, pebble accretion leaves its
imprint on the overall exoplanet population as a depletion of planets with
intermediate compositions, carving a valley in planet density for all spectral
types (abridged).
