  In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as
the variation of the gravitational Chern-Simons action with respect to the
metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved.
Performing a reduction of the Cotton tensor with respect to Carrollian
diffeomorphisms in a suitable frame, one discloses four sets of Cotton
Carrollian relatives, which are conformal and obey Carrollian conservation
equations. Each set of Carrollian Cotton tensors is alternatively obtained as
the variation of a distinct Carroll-Chern-Simons action with respect to the
degenerate metric and the clock form of a strong Carroll structure. The four
Carroll-Chern-Simons actions emerge in the Carrollian reduction of the original
Chern-Simons ascendant. They inherit its anomalous behaviour under
diffeomorphisms and Weyl transformations. The extremums of these Carrollian
actions are commented and illustrated.
