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Using density functional theory implemented within a tight-binding linear muffin-tin orbital method we perform calculations of electronic, magnetic, and transport properties of ferromagnetic free-standing fcc Co wires with diameters up to 1.5 nm. We show that finite-size effects play an important role in these nanowires resulting in oscillatory behavior of electronic charge and the magnetization as a function of the wire thickness, and a nonmonotonic behavior of spin-dependent quantized conductance. We calculate the magnetoresistance (MR) of a domain wall (DW) modeled by a spin-spiral region of finite width sandwiched between two semi-infinite Co wire leads. We find that the DW MR decreases very rapidly, on the scale of a few interatomic layers, with the increasing DW width. The largest MR value of about 250% is predicted for an abrupt DW in the monatomic wire. We show that, for some energy values, the density of states and the conductance may be nonzero only in one spin channel, making the MR for the abrupt DW infinitely large. We also demonstrate that for the abrupt DW a large MR may occur due to the hybridization between two spin subbands across the DW interface. We do not find, however, such a behavior at the Fermi energy for the Co wires considered.