The abelian sandpile model (ASM) was introduced by \textit{P. Bak, C. Tang} and \textit{K. Wiesenfield} [Self-organized criticality. Phys. Rev. A 38, 364--374 (1988)]. It is a dynamical model in which dynamics drives a system towards a stationary state characterized by power law correlations. Thus far to prove this fact rigorously was possible only in 1D. Present work was inspired by earlier work by \textit{S. N. Majumdar} and \textit{D. Dhar} [Equivalence between the Abelian sandpile model and the \(q\to 0\) limit of the Potts model. Physica A 185, 129-145 (1992)] in which these authors demonstrated the equivalence between the ASM and \(q\to 0\) limit of the Potts model which, as is well known, produces the spaning tree configurations. Let \(\nu_\Lambda\) be a uniform measure on a set of recurrent states then, because of the mentioned equivalence, it can be mapped onto the uniform spanning tree measure on \(\Lambda\) for as long as the dimensionality d lies between 2 and 4. The arguments need serious adjustment for d greater than 4. Both cases were studied in this work