The X -band electron paramagnetic resonance in La0.5 Ca0.5 MnO3 was studied. Fitting the measured temperature dependence of the EPR linewidth and intensity to established models were employed to probe the effects of finite-size and nonstoichiometry. Regarding these effects, the complex mixed magnetic ordering inherent in bulk samples was shown to be unstable. The antiferromagnetic (AFM) and charge ordered component is suppressed in nanosamples. But the ferromagnetic (FM) state, appearing in nanograins, is frustrated due to (i) an AFM-like core-shell interaction and (ii) a strong spin disorder at the surfaces and core-shell transition layers. In addition, a weak nonstoichiometry which does not affect the crystal structure in bulk induces a strong decrease of the FM component in its magnetic ground state.