The effects of poloidal asymmetries and heated minority species are shown to be necessary to accurately describe heavy impurity transport in present experiments in JET and ASDEX Upgrade. Plasma rotation, or any small background electrostatic field in the plasma, such as that generated by anisotropic external heating can generate strong poloidal density variation of heavy impurities. These asymmetries have recently been added to numerical tools describing both neoclassical and turbulent transport, and can increase neoclassical tungsten transport by an order of magnitude. Modelling predictions of the steady-state two-dimensional tungsten impurity distribution are compared with tomography from soft X-ray diagnostics. The modelling identities neoclassical transport enhanced by poloidal asymmetries as the dominant mechanism responsible for tungsten accumulation in the central core of the plasma. Depending on the bulk plasma profiles, turbulent diffusion and neoclassical temperature screening can prevent accumulation. Externally heated minority species can significantly enhance temperature screening in ICRH plasmas.