We investigate the transport properties of three-terminal carbon-based nanojunctions within the scattering matrix approach. The stability of such junctions is subordinated to the presence of nonhexagonal arrangements in the molecular network. Such ``defective'' arrangements do influence the resulting quantum transport observables, as a consequence of the possibility of acting as pinning centers of the corresponding wave function. By investigating a fairly wide class of junctions we have found regular mutual dependences between such localized states at the carbon network and a striking behavior of the conductance. In particular, we have shown that Fano resonances emerge as a natural result of the interference between defective states and the extended continuum background. As a consequence, the currents through the junctions hitting these resonant states might experience variations on a relevant scale with current modulations of up to 75%.