Some properties of magnetized two flavor color superconducting (2SC) cold dense quark matter under compact star conditions (COSC) are investigated within a $SU(2)_f$ Nambu Jona-Lasinio type model. We study the phase diagram for several model parametrizations. The features of each phase are analyzed through the behavior of the chiral and superconducting condensates for increasing chemical potential or magnetic field. We show how the phases are modified in the presence of $beta$-equilibrium as well as color and electric charge neutrality conditions.
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