  The interest in the structure of ice-rich planetary bodies, in particular the
differentiation between ice and rock, has grown due to the discovery of Kuiper
belt objects and exoplanets. We thus carry out a parameter study for a range of
planetary masses $M$, yielding radii $50 \aplt R \aplt 3000$~km, and for
rock/ice mass ratios between 0.25 and 4, evolving them for 4.5~Gyr in a cold
environment, to obtain the present structure. We use a thermal evolution model
that allows for liquid and vapor flow in a porous medium, solving mass and
energy conservation equations under hydrostatic equilibrium for a spherical
body in orbit around a central star. The model includes the effect of pressure
on porosity and on the melting temperature, heating by long-lived radioactive
isotopes, and temperature-dependent serpentinization and dehydration. We obtain
the boundary in parameter space [size, rock-content] between bodies that
differentiate, forming a rocky core, and those which remain undifferentiated:
small bodies, bodies with a low rock content, and the largest bodies
considered, which develop high internal pressures and barely attain the melting
temperature. The final differentiated structure comprises a rocky core, an
ice-rich mantle, and a thin dense crust below the surface. We obtain and
discuss the bulk density-radius relationship. The effect of a very cold
environment is investigated and we find that at an ambient temperature of
$\sim$20~K, small bodies preserve the ice in amorphous form to the present.
