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 that 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 an F1F2S structure, where a half-metallic ferromagnet F1 adjoins a weaker conventional ferromagnet F2. The current is injected through the F1 layer by means of an applied bias voltage. The second configuration involves an SF1F2F3S Josephson junction whereby a phase difference Δφ between the two superconducting electrodes generates the supercurrent flow. In this case, the central half-metallic F2 layer is surrounded by two weak ferromagnets F1 and F3. 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 θ in the F layers. We find that the bias-induced equal-spin triplet pairs are maximized in the half metal for θ≈90â 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 0.1EF. For the half-metallic Josephson junctions we often find that the spin current flowing in the half metal is equivalent to the charge supercurrent flowing throughout the junction. This is indicative that the current consists of spin-polarized triplet pairs. The conversion process of the opposite-spin triplet pairs to the equal-spin triplet pairs in the weaker magnets is clearly demonstrated. This is exemplified by the fact that the supercurrent in the half metal was found to be relatively insensitive to its thickness.