The magnetic properties of ~40 nm Nd(0.5)Ca(0.5)MnO(3) and Sm(0.5)Sr(0.5)MnO(3) nanoparticles are investigated by magnetometry and electronic spin resonance (ESR) spectroscopy. It is found that although their bulk counterparts have quite different magnetic properties at low temperatures, both the nanoparticles exhibit very similar magnetic behaviors, where the charge ordered transitions disappear and weak ferromagnetism emerges below about 100 K. A detailed analysis on the magnetic susceptibilities and the ESR linewidths reveals that for the two compounds the size reduction weakens both the ferromagnetic and antiferromagnetic interactions, and converts the long-range charge orderings to short-range ones. Moreover, the strength of the charge ordered correlations is observed to be not much affected by the size reduction. Based on the present results and the previous studies on various nanosized half-doped manganites, the magnetic phase diagram of the half-doped manganites with the particle sizes of ~25-40 nm is established. We find that this diagram is very similar to those for the bulk near half-doped manganites with large quenched disorder, which allows us to propose that the reported exotic phenomena in the nanosized half-doped manganites should be mainly ascribed to surface disorder effect. These results may provide a deeper insight into the role of size reduction on the physics of half-doped manganites.