  A Sierpinski gasket fractal network model is studied in respect of its
electronic spectrum and magneto-transport when each arm of the gasket is
replaced by a diamond shaped Aharonov-Bohm interferometer, threaded by a
uniform magnetic flux. Within the framework of a tight binding model for
non-interacting, spinless electrons and a real space renormalization group
method we unravel a class of extended and localized electronic states. In
particular, we demonstrate the existence of extreme localization of electronic
states at a special finite set of energy eigenvalues, and an infinite set of
energy eigenvalues where the localization gets delayed in space (staggered
localization). These eigenstates exhibit a multitude of localization areas. The
two terminal transmission coefficient and its dependence on the magnetic flux
threading each basic Aharonov-Bohm interferometer is studied in details. Sharp
switch on- switch off effects that can be tuned by controlling the flux from
outside, are discussed. Our results are analytically exact.
