We investigate the charge and spin transport in half-metallic ferromagnet ($F$) and superconductor ($S$) nanojunctions. We utilize a self-consistent microscopic method that can accommodate the broad range of energy scales present, and ensures proximity effects that account for the interactions at the interfaces are accurately determined. Two experimentally relevant half-metallic junction types are considered: The first is a $F_1 F_2 S$ structure, where a half-metallic ferromagnet $F_1$ adjoins a weaker conventional ferromagnet $F_2$. The current is injected through the $F_1$ layer by means of an applied bias voltage. The second configuration involves a $S F_1 F_2 F_3 S$ Josephson junction whereby a phase difference $Deltavarphi$ between the two superconducting electrodes generates the supercurrent flow. In this case, the central half-metallic $F_2$ layer is surrounded by two weak ferromagnets $F_1$ and $F_3$. By placing a ferromagnet with a weak exchange field adjacent to an $S$ layer, we are able to optimize the conversion process in which opposite-spin triplet pairs are converted into equal-spin triplet pairs that propagate deep into the half-metallic regions in both junction types. For the tunnel junctions, we study the bias-induced local magnetization, spin currents, and spin transfer torques for various orientations of the relative magnetization angle $theta$ in the $F$ layers. We find that the bias-induced equal-spin triplet pairs are maximized in the half-metal for $thetaapprox90^circ$ and as part of the conversion process, are anticorrelated with the opposite-spin pairs. We show that the charge current density is maximized, corresponding to the occurrence of a large amplitude of equal-spin triplet pairs, when the exchange interaction of the weak ferromagnet is about $0.1E_F.$
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