  Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where
stage $n$ is a non-negative integer. For any given vertex $x$ of SG(n), we
derive rigorously the probability distribution of the degree $j \in
\{1,2,3,4\}$ at the vertex and its value in the infinite $n$ limit. Adding up
such probabilities of all the vertices divided by the number of vertices, we
obtain the average probability distribution of the degree $j$. The
corresponding limiting distribution $\phi_j$ gives the average probability that
a vertex is connected by 1, 2, 3 or 4 bond(s) among all the spanning tree
configurations. They are rational numbers given as $\phi_1=10957/40464$,
$\phi_2=6626035/13636368$, $\phi_3=2943139/13636368$, $\phi_4=124895/4545456$.
