  We discuss holographic models of extremal and non-extremal black holes in
contact with a bath in d dimensions, based on a brane world model introduced in
arXiv:2006.04851. The main benefit of our setup is that it allows for a high
degree of analytic control as compared to previous work in higher dimensions.
We show that the appearance of quantum extremal islands in those models is a
consequence of the well-understood phase transition of RT surfaces, and does
not make any direct reference to ensemble averaging. For non-extremal black
holes the appearance of quantum extremal islands has the right behaviour to
avoid the information paradox in any dimension. We further show that for these
models the calculation of the full Page curve is possible in any dimension. The
calculation reduces to numerically solving two ODEs. In the case of extremal
black holes in higher dimensions, we find no quantum extremal islands for a
wide range of parameters. In two dimensions, our results agree with
arXiv:1910.11077 at leading order; however a finite UV cutoff introduced by the
brane results in subleading corrections. For example, these corrections result
in the quantum extremal surfaces moving further outward from the horizon, and
shifting the Page transition to a slightly earlier time.
