P-Stars are a new class of compact stars made of up and down quarks in β-equilibrium with electrons in an Abelian chromomagnetic condensate. We show that P-Stars are able to account for compact stars with R≲6 Km , as well as stars with radius comparable with canonical Neutron Stars. We find that cooling curves of P-Stars compare rather well with observational data. We suggest that P-Matter produced at the primordial deconfinement transition is a viable candidate for baryonic Cold Dark Matter. Finally, we show that P-Stars are able to overcome the gravitational collapse even for masses much greater than 106 M⊙.