The recent accomplishments in the design of molecular nanowires characterised by an increasing conductance with length has embarked the origin of extraordinary new family of molecular junctions referred to as "anti-ohmic" wires. Herein, this highly desirable, non-classical behavior, has been examined for the longer enough molecules exhibiting pronounced diradical character in their ground state within the unrestricted DFT formalism with spin and spatial symmetry breaking. We demonstrate that highly conjugated acenes signals higher resistance in open-shell singlet (OSS) configuration as compared to their closed-shell counterparts. This anomaly has been further put to proof for experimentally certified cumulene wires, which reveals phenomenal modulation in the transport characteristics such that an increasing conductance is observed in closed-shell limit, while higher cumulenes in OSS ground state yields a regular decay of conductance.