  We have made a calculation of the propagation of positrons from dark-matter
particle annihilation in the Galactic halo in different models of the dark
matter halo distribution using our 3D code, and present fits to our numerical
propagation Green's functions. We show that the Green's functions are not very
sensitive to the dark matter distribution for the same local dark matter energy
density. We compare our predictions with computed cosmic ray positron spectra
(``background'') for the ``conventional'' CR nucleon spectrum which matches the
local measurements, and a modified spectrum which respects the limits imposed
by measurements of diffuse Galactic gamma-rays, antiprotons, and positrons. We
conclude that significant detection of a dark matter signal requires favourable
conditions and precise measurements unless the dark matter is clumpy which
would produce a stronger signal. Although our conclusion qualitatively agrees
with that of previous authors, it is based on a more realistic model of
particle propagation and thus reduces the scope for future speculations.
Reliable background evaluation requires new accurate positron measurements and
further developments in modelling production and propagation of cosmic ray
species in the Galaxy.
