We predicted the existence of five carbon nanoribbons based on POPGraphene, by first-principles calculations. We investigated the role of the shape of the edges in stability, structural, electronic, and transport properties. Density functional theory (DFT) was implemented to relax the unit cell nanoribbons, and DFT combined with non-equilibrium Greens functions was used to obtain the transport properties of molecular devices. Our results strongly suggest that all nanoribbons are stable, and can be feasibly obtained through experiment. Furthermore, the edge termination with pentarings is an important factor in the stability of nanoribbons. The electronic properties show that the three zigzag nanoribbons have a metallic behavior and the two armchair ones are semiconductors, but with a very tiny indirect bandgap of 0.053 eV and 0.050 eV. The transport properties show that the presence of partially filled steep bands crossing deeper into the Fermi level triggers high conductivity in molecular devices and the presence of flat bands decreases the device conductivity. The presence of sub-bandgap regions triggers the rise of negative differential resistance (NDR) regions in the device operation. The molecular device behavior is strongly dependent on the shape of the edges, presenting characteristics of field effect transistors (FETs), lighting emitting diodes (LEDs), or resonant tunneling diodes (RTDs), depending on the edge termination and operation range.