We present a systematic quantitative description of the magnetoconductance of split-gate quantum wires focusing on formation and evolution of the odd (spin-resolved) conductance plateaus. We start from the case of spinless electrons where the calculated magnetoconductance in the Hartree approximation shows the plateaus quantized in units of 2 e2 /h separated by transition regions, whose width grows as the magnetic field is increased. We show that the transition regions are related to the formation of the compressible strips in the middle of the wire occupied by electrons belonging to the highest (spin-degenerate) subband. Accounting for the exchange and correlation interactions within the spin density functional theory (DFT) leads to the lifting of the spin degeneracy and formation of the spin-resolved plateaus at odd values of e2 /h. The most striking feature of the magnetoconductance is that the width of the odd conductance steps in the spin DFT calculations is equal to the width of the transition intervals between the conductance steps in the Hartree calculations. A detailed analysis of the evolution of the Hartree and the spin DFT subband structure provides an explanation of this finding. Our calculations also reveal the effect of the collapse of the odd conductance plateaus for lower fields. We attribute this effect to the reduced screening efficiency in the confined (wire) geometry when the width of the compressible strip in the center becomes much smaller than the extent of the wave function. A detailed comparison to the experimental data demonstrates that the spin DFT calculations reproduce not only qualitatively but also quantitatively all the features observed in the experiment. This includes the dependence of the width of the odd and even plateaus on the magnetic field as well as the estimation of the subband index corresponding to the last resolved odd plateau in the magnetoconductance. © 2008 The American Physical Society.