  We constrain the initial stage of the reionization process around progenitors
of galaxies, such as the extent of the initial HII region before its fusion
with the UV background and the duration of its propagation. We use a set of
reionisation simulations with different resolutions and ionizing source
recipes. A catalog of the HII regions properties is built thanks to a merger
tree of HII regions. We draw local reionization histories as a function of time
and investigate variations according to the halo mass progenitors of the
regions. We then extrapolate the halo mass inside the region from high z to z=0
to make predictions about the reionization histories of z=0 galaxies. We found
that the later an HII region appears, the smaller will be its related lifetime
and volume before it sees the global UV background. Quantitatively the duration
and the extent of the initial growth of an HII region is strongly dependent on
the mass of the inner halo and can be as long as 50 % of the reionization
epoch. We found that the most massive is a halo today, the earlier it appears
and the larger are the extension and the duration of propagation of its HII
region. Quantitative predictions differ depending on the box size or the source
model: small simulated volumes are affected by proximity effects between HII
regions and halo-based source models predict smaller regions and slower I-front
expansion than in models using star particles as ionizing sources. Our results
suggests that Milky Way-type halos have a maximal extent of 1.1 Mpc/h for the
initial HII region that established itself in 150-200$\pm 20$ Myrs. This is
consistent with prediction made using constrained Local Group simulation.
Considering halos with masses comparable to those of the Local Group (MW+M31),
our result suggests that statistically it has not been influenced by an
external front coming from a Virgo-like cluster.
