A computer simulation study describing the electrophoretic separation and migration of methadone enantiomers in presence of free and immobilized (2-hydroxypropyl)-β-CD is presented. The 1:1 interaction of methadone with the neutral CD was simulated by using experimentally determined mobilities and complexation constants for the complexes in a low-pH BGE comprising phosphoric acid and KOH. The use of complex mobilities represents free solution conditions with the chiral selector being a buffer additive, whereas complex mobilities set to zero provide data that mimic migration and separation with the chiral selector being immobilized, that is CEC conditions in absence of unspecific interaction between analytes and the chiral stationary phase. Simulation data reveal that separations are quicker, electrophoretic displacement rates are reduced, and sensitivity is enhanced in CEC with on-column detection in comparison to free solution conditions. Simulation is used to study electrophoretic analyte behavior at the interface between sample and the CEC column with the chiral selector (analyte stacking) and at the rear end when analytes leave the environment with complexation (analyte destacking). The latter aspect is relevant for off-column analyte detection in CEC and is described here for the first time via the dynamics of migrating analyte zones. Simulation provides insight into means to counteract analyte dilution at the column end via use of a BGE with higher conductivity. Furthermore, the impact of EOF on analyte migration, separation, and detection for configurations with the selector zone being displaced or remaining immobilized under buffer flow is simulated. In all cases, the data reveal that detection should occur within or immediately after the selector zone.