We have performed a systematic study of the emergence of meta-stable states in density functional theory plus Hubbard U (DFT+U ) simulations of NiO, CoO, FeO. Particular attention is given to the spin-polarization of the exchange-correlation functional and the double counting term, and the role of the spin-orbit coupling... The method of occupation matrix control is extended to use constrained random density matrices to map out the local minima in the total energy landscape. The extended scheme, random density matrix control, is successfully benchmarked against UO2, one of the most investigated systems in the field. When applied to the transition metal oxides it yields several meta- stable states which are well-characterized by their local spin and orbital moments. We find that the addition of spin-orbit coupling helps the simulations to converge to the global high-spin energy minimum. The random density matrix control scheme combined with LDA+U yields accurate magnetic moments for all the studied AFM transition metal oxides. (read more)