Using first-principles density functional theory (DFT) calculations, we perform a systematic study on the structural stability, electronic, magnetic and transport properties of zigzag BNC nanoribbons (ZBNCNRs) consisting of boron–nitrogen (B–N) separated polyacene chains across the ribbon width. We focus on five different nanoribbon structures with various B–N chain edge types. The first and second structures are terminated by either B or N atoms on both sides, while third and fourth are terminated by boron and nitrogen atoms on opposite edges with both bare edge and hydrogen passivation, respectively. The fifth ZBNCNR contains hydrogen terminated carbon atoms on the opposite edges. We study the effect of different edges and varying ribbon widths on the structure, stability, electronic and magnetic properties of these systems. We find moderate cohesive energies and favourable formation energies for the ZBNCNRs, suggesting their mechanical stability and possible realization under suitable experimental conditions. Interestingly, we find the lowest formation energy for the H-passivated C-edged ZBNCNR among others, indicating its preferred formation feasibility. Our results show that, for all of the ZBNCNR widths, the ones with bare edges show metallic behaviour, while the others (systems with hydrogen passivated edges) exhibit semiconducting properties. Interestingly, we find that hydrogen passivated C-edge ZBNCNRs display a range of conducting properties, including half-metallic and metallic, depending on the ribbon width. We also explore the effect of external electric fields on the electronic structure of hydrogen passivated C-edge nanoribbons. Moreover, our electronic transport study on this most-stable half-metallic ZBNCNR shows strong spin filter properties up to a certain bias voltage and negative differential resistance behaviour at low-bias voltage, suggesting potential applications in electronic and spintronic devices.