In this paper, the flow splitting of fluids with complex rheological properties in complex geometries is examined. This work is motivated by the desire to achieve good control of flow-splitting processes independent of the geometries of the manifold. As an example of this class of flows, the flow of a complex fluid from a main pipe to two branch pipes is considered. Using the diameter and length of one branch as parameters, the flow splitting of Newtonian and power-law fluids was studied. This study was conducted under both isothermal and non-isothermal conditions; the latter were achieved by imposing a temperature difference between the wall and the inlet. Hence, the splitting of power-law fluids with temperature-dependent viscosity was also studied and compared with the isothermal cases. Our analytical and numerical results indicate that the unevenness in the split is accentuated as the geometrical asymmetry and degree of shear thinning increase. In the non-isothermal cases, symmetric splitting is approached as the ratio of inlet to wall viscosity increases. However, as this ratio is reduced below unity, asymmetric splitting is promoted.