  We present new models for the evolution of stars with mass in the range 1Msun
< M < 7.5Msun, followed from the pre-main-sequence through the asymptotic giant
branch phase. The metallicity adopted is $Z=3*10^{-4} (which, with an
alpha-enhancement of +0.4, corresponds to [Fe/H]=-2). Dust formation is
described by following the growth of dust grains of various types as the wind
expands from the stellar surface.
  Models with mass M>3Msun experience Hot Bottom Burning, thus maintaining the
surface C/O below unity. Unlike higher Z models, the scarcity of silicon
available in the envelope prevents the formation of silicates in meaningful
quantities, sufficient to trigger the acceleration of the wind via radiation
pressure on the dust grains formed. No silicate formation occurs below a
threshold metallicity of Z=10^{-3}.
  Low--mass stars, with M< 2.5Msun become carbon stars, forming solid carbon
dust in their surroundings. The total dust mass formed depends on the uncertain
extent of the inwards penetration of the convective envelope during the Third
Dredge--Up episodes following the Thermal Pulses. Carbon grains have sizes 0.08
micron < a_C < 0.12 micron and the total amount of dust formed (increasing with
the mass of the star) is M_C=(2-6)*10^{-4}Msun.
  Our results imply that AGB stars with Z=3*10^{-4} can only contribute to
carbon dust enrichment of the interstellar medium on relatively long
timescales, > 300 Myr, comparable to the evolutionary time of a 3Msun star. At
lower metallicities the scarcity of silicon available and the presence of Hot
Bottom Burning even in M< 2Msun, prevents the formation of silicate and carbon
grains. We extrapolate our conclusion to more metal--poor environments, and
deduce that at Z < 10^{-4} dust enrichment is mostly due to metal condensation
in supernova ejecta.
