We predict using first-principles calculations that recently synthesized C-BN nanostructures exhibit rich magnetic and electronic properties that are sensitive to system dimensionality and chirality. Due to different C-B(N) p(z)-orbital hybridization at the interface, two-dimensional zigzag C-BN sheets and one-dimensional zigzag nanoribbons show weak and strong magnetism respectively. Moreover, the band gap of the zigzag ribbons shows strong sensitivity to the edge magnetism and the BN concentration. For armchair systems, the band gap of the C-BN sheets and ribbons exhibits distinct variation trends with the changing BN concentration, correlating with the width of the adjacent graphene nanoribbon. (C) 2011 Elsevier B.V. All rights reserved.