  We have computed a grid of up-to-date stellar evolutionary models including
atomic diffusion, in order to study the evolution with time of the surface Li
abundance in low-mass metal-poor stars. We discuss in detail the dependence of
the surface Li evolution on the initial metallicity and stellar mass, and
compare the abundances obtained from our models with the available Li
measurements in Pop II stars. While it is widely accepted that the existence of
the Spite Li-plateau for these stars is a strong evidence that diffusion is
inhibited, we show that, when taking into account observational errors,
uncertainties in the Li abundance determinations, in the effective temperature
scale, and in particular the size of the observed samples of stars, the Spite
plateau and the Li abundances in subgiant branch stars can be reproduced also
by models including fully efficient diffusion, provided that the most
metal-poor field halo objects are between 13.5 and 14 Gyr old. We provide the
value of the minimum number of plateau stars to observe, for discriminating
between efficient or inhibited diffusion. From our models with diffusion we
derive that the average Li abundance along the Spite plateau is about a factor
of 2 lower than the primordial one. As a consequence, the derived primordial Li
abundance is consistent with a high helium and low deuterium Big Bang
Nucleosynthesis; this implies a high cosmological baryon density as inferred
from the analyses of the cosmic microwave background.
