  We investigate the occurrence of bound states in the continuum (BIC's) in
serial structures of quantum dots coupled to an external waveguide, when some
characteristic length of the system is changed. By resorting to a multichannel
scattering-matrix approach, we show that BIC's do actually occur in
two--dimensional serial structures, and that they are a robust effect. When a
BIC is produced in a two--dot system, it also occurs for several coupled dots.
We also show that the complex dependence of the conductance upon the geometry
of the device allows for a simple picture in terms of the resonance pole motion
in the multi--sheeted Riemann energy surface. Finally, we show that in
correspondence to a zero--width state for the open system one has a multiplet
of degenerate eigenenergies for the associated closed serial system, thereby
generalizing results previously obtained for single dots and two-dot devices.
