  We prove existence of solutions and study the nonlocal-to-local asymptotics
for nonlocal, convective, Cahn-Hilliard equations in the case of a W^{1,1}
convolution kernel and under homogeneous Neumann conditions. Any type of
potential, possibly also of double-obstacle or logarithmic type, is included.
Additionally, we highlight variants and extensions to the setting of periodic
boundary conditions and viscosity contributions, as well as connections with
the general theory of evolutionary convergence of gradient flows.
