  For technological purposes and theoretical curiosity, it is very interesting
to have a building block that produces a considerable amount of entanglement
between on-demand sites through a simple control of a few sites. Here, we
consider permanently-coupled spin networks and study entanglement generation
between qubit pairs to find low-complexity structures capable of generating
considerable entanglement between various qubit pairs. We find that in axially
symmetric networks the generated entanglement between some qubit pairs is
rather larger than generic networks. We show that in uniformly-coupled spin
rings each pair can be considerably entangled through controlling suitable
vertices. To set the location of controlling-vertices, we observe that the
symmetry has to be broken for a definite time. To achieve this, a magnetic flux
can be applied to break symmetry via Aharonov-Bohm effect. Such a set up can
serve as an efficient entanglement distributor bus in which each vertex-pair
can be efficiently entangled through exciting only one fixed vertex and
controlling the evolution time. The low-complexity of this scheme makes it
attractive for use in nanoscale quantum information processors.
