  A variety of open quantum networks are currently under intense examination to
model energy transport in photosynthetic systems. Here we study the coherent
transfer of a quantum excitation over a network incoherently coupled with a
structured and small environment that effectively models the photosynthetic
reaction center. Our goal is to distill a few basic, possibly universal,
mechanisms or "effects" that are featured in simple energy-transfer models. In
particular, we identify three different phenomena: the congestion effect, the
asymptotic unitarity and the staircase effects. We begin with few-site models,
in which these effects can be fully understood, and then proceed to study more
complex networks similar to those employed to model energy transfer in
light-harvesting complexes. Our numerical studies on such networks seem to
suggest that some of the effects observed in simple networks may be of
relevance for biological systems, or artificial analogues of them as well.
