  We consider two bidimensional random models characterised by the following
features: a) their Hamiltonians are separable in polar coordinates and b) the
random part of the potential depends either on the angular coordinate or on the
radial one, but not on both. The disorder correspondingly localises the angular
or the radial part of the eigenfunctions. We analyse the analogies and the
differences which exist between the selected 2D models and their 1D
counterparts. We show how the analogies allow one to use correlated disorder to
design a localisation length with pre-defined energy dependence and to produce
directional localisation of the wavefunctions in models with angular disorder.
We also discuss the importance of finite-size and resonance effects in shaping
the eigenfunctions of the model with angular disorder; for the model with
disorder associated to the radial variable we show under what conditions the
localisation length coincides with the expression valid in the 1D case.
