  We study the quantum dynamics of a photo-excitation uniformly distributed at
the periphery of an extended star network (with $N_B$ branches of length
$L_B$). More specifically, we address here the question of the energy
absorption at the core of the network and how this process can be improved (or
not) by the inclusion of peripheral defects with a tunable energy amplitude
$\Delta$. Our numerical simulations reveal the existence of optimal value of
energy defect $\Delta^*$ which depends on the network architecture. Around this
value, the absorption process presents a strong speedup (i.e. reduction of the
absorption time) provided that $L_B \leq L_B^*$ with $L_B^* \approx
12.5/\ln(N_B) $. Analytical/numerical developments are then conducted to
interpret this feature. We show that the origin of this speedup takes place in
the hybridization of two upper-band excitonic eigenstates. This hybridization
is important when $L_B \leq L_B^*$ and vanishes almost totally when $L_B >
L_B^*$. These structural rules we draw here could represent a potential guide
for the practical design of molecular nano-network dedicated to the realisation
of efficient photo-excitation absorption.
