Abstract
Potential theory on a Cartier tree T is developed on the lines of the classical and the axiomatic theories on harmonic spaces. The harmonic classifications of such trees are considered; the notion of a subordinate structure on T is introduced to consider more generally the potential theory on T associated with the Schrodinger equation Delta u(x) = Q(x)u(x), Q(x) >= 0 on T; polysuperharmonic functions and polypotentials on T are defined and a Riesz-Martin representation for positive polysuperharmonic functions is obtained.