  The recently developed MOTSodesic method for locating marginally outer
trapped surfaces was effectively restricted to non-rotating spacetimes. In this
paper we extend the method to (multi-)axisymmetric time slices of
(multi-)axisymmetric spacetimes of any dimension. We then apply this method to
study marginally outer trapped surfaces (MOTSs) in the BTZ, Kerr and
Myers-Perry black holes. While there are many similarities between the MOTSs
observed in these spacetimes and those seen in Schwarzschild and
Reissner-Nordstr\"om, details of the more complicated geometries also introduce
some new, previously unseen, behaviours.
