  We study the structure and dynamics of entanglement in CFTs and black holes.
We use a local entanglement measure, the entanglement contour, which is a
spatial density function for von Neumann entropy with some additional
properties. The entanglement contour can be calculated in many 1+1d condensed
matter systems and simple models of black hole evaporation. We calculate the
entanglement contour of a state excited by a splitting quench, and find
universal results for the entanglement contours of low energy non-equilibrium
states in 2d CFTs. We also calculate the contour of a non-gravitational bath
coupled to an extremal AdS$_2$ black hole, and find that the contour only has
finite support within the bath, due to an island phase transition. The
particular entanglement contour proposal we use quantifies how well the bath's
state can be reconstructed from its marginals, through its connection to
conditional mutual information, and the vanishing contour is a reflection of
the protection of bulk island regions against erasures of the boundary state.
