  We prove the existence and describe limiting curves resulting from deviations
in partial sums in the ergodic theorem for cylindrical functions and polynomial
(self-similar) adic systems. For a general ergodic measure-preserving
transformation and a summable function we give a necessary condition for a
limiting curve to exist. Our work generalizes results by \'E. Janvresse, T. de
la Rue and Y. Velenik and answers several questions from their work.
