In a previous paper [Nat. Photon. 5, 166 (2011)], we reported on a planar dielectric antenna that achieved 96% efficiency in collecting the photons emitted by a single molecule. In that work, the transition dipole moment of the molecule was set perpendicular to the antenna plane. Here, we present a theoretical extension of that scheme that reaches collection efficiencies beyond 99% for emitters with arbitrarily oriented dipole moments. Our work opens important doors in a wide range of contexts including quantum optics, quantum metrology, nanoanalytics, and biophysics. In particular, we provide antenna parameters to realize ultrabright single-photon sources in high-index materials such as semiconductor quantum dots and color centers in diamond, as well as sensitive detection of single molecules in nanofluidic devices.