  We compute the mass and composition of dust produced by stars with masses in
the range 1Msun<M<8 Msun and with a metallicity of Z=0.001 during their AGB and
Super AGB phases. Stellar evolution is followed from the pre-main sequence
phase using the code ATON which provides, at each timestep, the thermodynamics
and the chemical stucture of the wind. We use a simple model to describe the
growth of the dust grains under the hypothesis of a time-independent,
spherically symmetric stellar wind. We find that the total mass of dust
injected by AGB stars in the interstellar medium does not increase
monotonically with stellar mass and ranges between a minimum of 10^{-6}Msun for
the 1.5Msun stellar model, up to 2x10^{-4} Msun, for the 6Msun case. Dust
composition depends on the stellar mass: low-mass stars (M < 3Msun) produce
carbon-rich dust, whereas more massive stars, experiencing Hot Bottom Burning,
never reach the carbon-star stage, and produce silicates and iron. This is in
partial disagreement with previous investigations in the literature, which are
based on synthetic AGB models and predict that, when the initial metallicity is
Z=0.001, C-rich dust is formed at all stellar masses. The differences are due
to the different modelling of turbulent convection in the super-adiabaticity
regime. Also in this case the treatment of super-adiabatic convection shows up
as the most relevant issue affecting the dust-formation process. We also
investigate Super AGB stars with masses 6.5Msun<M<8 Msun that evolve over a ONe
core.Due to a favourable combination of mass loss and Hot Bottom Burning, these
stars are predicted to be the most efficient silicate-dust producers, releasing
[2 - 7]x 10^{-4} Msun masses of dust. We discuss the robustness of these
predictions and their relevance for the nature and evolution of dust at early
cosmic times.
