  We construct the boundary phase space in $D$-dimensional Einstein gravity
with a generic given co-dimension one null surface ${\cal N}$ as the boundary.
The associated boundary symmetry algebra is a semi-direct sum of
diffeomorphisms of $\cal N$ and Weyl rescalings. It is generated by $D$ towers
of surface charges that are generic functions over $\cal N$. These surface
charges can be rendered integrable for appropriate slicings of the phase space,
provided there is no graviton flux through $\cal N$. In one particular slicing
of this type, the charge algebra is the direct sum of the Heisenberg algebra
and diffeomorphisms of the transverse space, ${\cal N}_v$ for any fixed value
of the advanced time $v$. Finally, we introduce null surface expansion- and
spin-memories, and discuss associated memory effects that encode the passage of
gravitational waves through $\cal N$, imprinted in a change of the surface
charges.
