  [Abridged] We calculate the structural evolution and nucleosynthesis of a
grid of models covering the metallicity range: -6.5 < [Fe/H] < -3.0 (plus Z=0),
and mass range: 0.85 < M < 3.0 Msun, amounting to 20 stars in total. In this
paper, the first of a series describing and analysing this large data set, we
present the resulting stellar yields. Many of the models experience violent
nuclear burning episodes not seen at higher metallicities. We refer to these
events as `Dual Flashes'. These events have also been reported by previous
studies. Some of the material processed by the Dual Flashes is dredged up
causing significant surface pollution with a distinct chemical composition. We
also analyse the yields in terms of C and N, comparing them to the observed
CEMP abundances. At the lowest metallicities ([Fe/H] < -4.0) we find the yields
to contain ~1 to 2 dex too much carbon, in agreement with all previous studies.
At higher metallicities ([Fe/H] = -3.0), where the observed data set is much
larger, all our models produce yields with [C/Fe] values consistent with those
observed in the most C-rich CEMPs. However it is only the low-mass models that
undergo the Dual Shell Flash (which occurs at the start of the TPAGB) that can
best reproduce the C and N observations. Normal Third Dredge-Up can not
reproduce the observations because at these metallicities intermediate mass
models (M > 2 Msun) suffer HBB which converts the C to N thus lowering [C/N]
well below the observations, whilst if TDU were to occur in the low-mass (M < 1
Msun) models (we do not find it to occur in our models), the yields would be
expected to be C-rich only, which is at odds with the `dual pollution' of C and
N generally observed in the CEMPs.
