We present asymptotic giant branch (AGB) models of metallicity $Z=10^{-4}$ and $Z=3times 10^{-4}$, with the aim of understanding how the gas enrichment and the dust production change in very metal-poor environments and to assess the general contribution of AGB stars to the cosmic dust yield. The stellar yields and the dust produced are determined by the change in the surface chemical composition, with a transition occurring at $sim 2.5~M_{odot}$. Stars of mass $M < 2.5~M_{odot}$ reach the carbon stage and produce carbon dust, whereas their higher mass counterparts produce mainly silicates and alumina dust; in both cases the amount of dust manufactured decreases towards lower metallicities. The $Z=10^{-4}$ models show a complex and interesting behaviour on this side, because the efficient destruction of the surface oxygen favours the achievement of the C-star stage, independently of the initial mass. The present results might indicate that the contribution from this class of stars to the overall dust enrichment in metal-poor environments is negligible at redshifts $z>5$.
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