  Localization-delocalization transition in a discrete Anderson nonlinear
Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$
similar to a percolation transition on a disordered lattice, with the
nonlinearity parameter thought as the control parameter. In vicinity of the
critical point the spreading of the wave field is subdiffusive in the limit
$t\rightarrow+\infty$. The second moment grows with time as a powerlaw $\propto
t^\alpha$, with $\alpha$ exactly 1/3. This critical spreading finds its
significance in some connection with the general problem of transport along
separatrices of dynamical systems with many degrees of freedom and is
mathematically related with a description in terms fractional derivative
equations. Above the delocalization point, with the criticality effects
stepping aside, we find that the transport is subdiffusive with $\alpha = 2/5$
consistently with the results from previous investigations. A threshold for
unlimited spreading is calculated exactly by mapping the transport problem on a
Cayley tree.
