Density peaking in source-free L-mode plasmas with Lower Hybrid Curren Drive (LHCD) is observed to increase with increasing peaking of the current profile. For the discharges investigated, the relationship can be summarised as ne0/<ne>≅1.2li, where li is the normalised internal inductance. These observations are strongly supportive of theories explaining particle convection by the Curvature Pinch or Turbulent Equipartition. They were made in a series of MHD-quiescent LHCD plasmas, including positive and negative central magnetic shear, as well as fully current driven plasmas with negligible Ware pinch and no core particle source. No evidence was found of an Anomalous Thermodiffusive contribution to the convective flux. ELMy H-modes, although NBI fuelled, have a qualitatively similar dependence of density peaking on shear.