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Aims.We study the growth of dust in oxygen-rich stellar outflows in order to find out to which extent dust growth models canquantitatively reconcile with the quantities and nature of dust as derived from observations of the infrared emission from circumstellardust shells.Methods.We use a set of nine well-observed massive supergiants with optically thin dust shells as testbeds because of the relativelysimple properties of the outflows from massive supergiants, contrary to the case of AGB stars. Models of the infrared emission fromtheir circumstellar dust shells are compared to their observed infrared spectra to derive the essential parameters that rule dust formationin the extended envelope of these stars. The results are compared with a model for silicate dust condensation.Results.For all objects, the infrared emission in the studied wavelength range, between 6μm and 25μm, can be reproduced rather wellby a mixture of non-stoichiometric iron-bearing silicates, alumina, and metallic iron dust particles. For three objects (μCep, RW Cyg,and RS Per), the observed spectra can be sufficiently well reproduced by a stationary and (essentially) spherically symmetric outflowin the instantaneous condensation approximation. For these objects, the temperature at the onset of massive silicate dust growth is ofthe order of 920 K and the corresponding outflow velocity of the order of the sound velocity. This condensation temperature is onlysomewhat below the vapourisation temperature of the silicate dust and suggests that the silicate dust grows on the corundum dustgrains that formed well inside of the silicate dust shell at a much higher temperature. The low expansion velocity at the inner edge ofthe silicate dust shell further suggests that, for these supergiants, the region inside the silicate dust shell has an only subsonic averageexpansion velocity, though a high degree of supersonic turbulence is indicated by the widths of spectral lines.Conclusions.Our results suggest that for the two major problems of dust formation in stellar outflows, that is (i) formation of seednuclei and (ii) their growth to macroscopic dust grains, we are gradually coming close to a quantitative understanding of the seconditem.