  The electronic transport through a triple quantum dot molecule attached in
parallel to leads in presence of a magnetic flux is studied. Analytical
expressions of the linear conductance and density of states for the molecule in
equilibrium at zero temperature are obtained. As a consequence of quantum
interference, the conductance exhibits in general a Breit--Wigner and two Fano
resonances, the positions and widths of which are controlled by the magnetic
field. Every two flux quanta, there is an inversion of roles of the bonding and
antibonding states. For particular values of the magnetic flux and dot-lead
couplings, one or even both Fano resonances collapse and bound states in the
continuum (BIC's) are formed. The line broadenings of the molecular states are
examined as a function of the Aharonov--Bohm phase around the condition for the
formation of BIC's, finding resonances extremely narrow and robust against
variations of the magnetic field.
