  One of the purposes of this paper is to clarify the strong analogy between
potential theory on the open unit disk and the homogeneous tree, to which we
dedicate an introductory section. We then exemplify this analogy by a study of
Riesz measures. Starting from interesting work by Favorov and Golinskii [A
Blaschke-type condition for analytic and subharmonic functions and application
to contraction operators. Linear and complex analysis, pp. 37-47, Amer. Math.
Soc. Transl. (2) 226, Amer. Math. Soc., Providence, RI, 2009], we consider
subharmonic functions on the open unit disk, resp. on the homogenous tree.
Supposing that we can control the way how those functions may tend to infinity
at the boundary, we derive moment type conditions for the Riesz measures. One
one hand, we generalise the previous results for the disk, and on the other
hand, we show how to obtain analogous results in the discrete setting of the
tree.
