  We study causal wedges associated with a given sub-region in the boundary of
asymptotically AdS spacetimes. Part of our motivation is to better understand
the recently proposed holographic observable, causal holographic information
(CHI), which is given by the area of a bulk co-dimension two surface lying on
the boundary of the causal wedge. It has been suggested that CHI captures the
basic amount of information contained in the reduced density matrix about the
bulk geometry. To explore its properties further we examine its behaviour in
time-dependent situations. As a simple model we focus on null dust collapse in
an asymptotically AdS spacetime, modeled by the Vaidya-AdS geometry. We argue
that while CHI is generically quasi-telelogical in time-dependent backgrounds,
for suitable choice of sub-regions in conformal field theories, the temporal
evolution of CHI is entirely causal. We comment on the implications of this
observation and more generally on features of causal constructions and contrast
our results with the behaviour of holographic entanglement entropy. Along the
way we also derive the rate of early time growth and late time saturation (to
the thermal value) of both CHI and entanglement entropy in these backgrounds.
