  In the first part of this paper we shall classify proper triharmonic
isoparametric surfaces in 3-dimensional homogeneous spaces
(Bianchi-Cartan-Vranceanu spaces, shortly BCV-spaces). We shall also prove that
triharmonic Hopf cylinders are necessarily CMC. In the last section we shall
determine a complete classification of CMC r-harmonic Hopf cylinders in
BCV-spaces, r>=3. This result ensures the existence, for suitable values of r,
of an ample family of new examples of r-harmonic surfaces in BCV-spaces.
