Split-flow thin (SPLITT) fractionation devices have been widely used to separate macromolecules, colloids, cells and particles. Recently, the quadrupole magnetic flow sorter (QMS) has been reported in the literature as another family of SPLITT fractionation device. However, the separation performance observed in the experimental measurements is generally found to deviate from the ideal behaviour. Possible causes such as hydrodynamic lift force, high particle concentration and imperfect geometries have been extensively examined. However, the effects of flow development regions and fringing magnetic force field at the separation channel inlet and outlet, which are ignored by the theory, have not been investigated. The error introduced by ignoring these effects need to be rigorously studied so that the theory can be used to optimise operation flow rates with confidence. Indeed, we find in this paper that these ignored effects are responsible to the discrepancy between the experimental data and the theoretical predictions. A new theory has been proposed for optimisation of device operation.