  We study the halo mass accretion history (MAH) and its correlation with the
internal structural properties in coupled dark energy cosmologies (cDE). To
accurately predict all the non-linear effects caused by dark interactions, we
use the COupled Dark Energy Cosmological Simulations (CoDECS). We measure the
halo concentration at z=0 and the number of substructures above a mass
resolution threshold for each halo. Tracing the halo merging history trees back
in time, following the mass of the main halo, we develope a MAH model that
accurately reproduces the halo growth in term of M_{200} in the {\Lambda}CDM
Universe; we then compare the MAH in different cosmological scenarios. For cDE
models with a weak constant coupling, our MAH model can reproduce the
simulation results, within 10% of accuracy, by suitably rescaling the
normalization of the linear matter power spectrum at z=0, {\sigma}_8. However,
this is not the case for more complex scenarios, like the "bouncing" cDE model,
for which the numerical analysis shows a rapid growth of haloes at high
redshifts, that cannot be reproduced by simply rescaling the value of
{\sigma}_8. Moreover, at fixed value of {\sigma}_8, cold dark matter (CDM)
haloes in these cDE scenarios tend to be more concentrated and have a larger
amount of substructures with respect to {\Lambda}CDM predictions. Finally, we
present an accurate model that relates the halo concentration to the time at
which it assembles half or 4% of its mass. Combining this with our MAH model,
we show how halo concentrations change while varying only {\sigma}_8 in a
{\Lambda}CDM Universe, at fixed halo mass.
