  We study the distribution of sizes of erased loops for loop-erased random
walks on regular and fractal lattices. We show that for arbitrary graphs the
probability $P(l)$ of generating a loop of perimeter $l$ is expressible in
terms of the probability $P_{st}(l)$ of forming a loop of perimeter $l$ when a
bond is added to a random spanning tree on the same graph by the simple
relation $P(l)=P_{st}(l)/l$. On $d$-dimensional hypercubical lattices, $P(l)$
varies as $l^{-\sigma}$ for large $l$, where $\sigma=1+2/z$ for $1<d<4$, where
z is the fractal dimension of the loop-erased walks on the graph. On
recursively constructed fractals with $\tilde{d} < 2$ this relation is modified
to $\sigma=1+2\bar{d}/{(\tilde{d}z)}$, where $\bar{d}$ is the hausdorff and
$\tilde{d}$ is the spectral dimension of the fractal.
