Numerical calculations of thermochemical convection in a rotating, electrically conducting fluid sphere with heterogeneous boundary conditions are used to model effects of asymmetric inner core growth. With heterogeneous inner core growth but no melting, outer core flow consists of intense convection where inner core buoyancy release is high, weak convection where inner core buoyancy release is low, and large scale, mostly westward flow in the form of spiraling gyres. With localized inner core melting, outer core flow includes a gravity current of dense fluid that spreads over the inner core boundary, analogous to the seismic F-layer. An analytical model for gravity currents on a sphere connects the structure of the dense layer to the distribution of inner core melting and solidification. Predictions for F-layer formation by asymmetric inner core growth include large-scale asymmetric gyres below the core-mantle boundary and eccentricity of the geomagnetic field.