Magnetic properties of a large assembly of ultrathin graphitic particles obtained by heavy sonication of graphite powder dispersed in N-methylpyrrolidone were measured by electron-spin resonance (ESR). The ESR signal was decomposed into one narrow and one broad component. The narrow component was associated with localized Curie-type defects. The temperature dependence of the predominant broad component points to a transition to a superparamagnetic-like state at 25 K. By performing the density-functional-theory calculations for graphene with selected extended defects (the sheet edges, zigzag chains of chemisorbed H atoms, and pentagon-octagon rows), we found considerable magnetic moments at C atoms in their vicinities. We attribute the magnetism in the graphitic particles to the localized electronic states near the defects in the network of the p electrons of graphene. The ferromagnetic (FM) correlations among magnetic moments at carbon atoms near the edges are not able to give rise to a long-range FM order.