  The leaky abelian sandpile model (Leaky-ASM) is a growth model in which $n$
grains of sand start at the origin in $\mathbb{Z}^2$ and diffuse along the
vertices according to a toppling rule. A site can topple if its amount of sand
is above a threshold. In each topple a site sends some sand to each neighbor
and leaks a portion $1-1/d$ of its sand. We compute the limit shape as a
function of $d$ in the symmetric case where each topple sends an equal amount
of sand to each neighbor. The limit shape converges to a circle as $d\to 1$ and
a diamond as $d\to\infty$. We compute the limit shape by comparing the odometer
function at a site to the probability that a killed random walk dies at that
site. When $d\to 1$ the Leaky-ASM converges to the abelian sandpile model (ASM)
with a modified initial configuration. We also prove the limit shape is a
circle when simultaneously with $n\to\infty$ we have that $d=d_n$ converges to
$1$ slower than any power of $n$. To gain information about the ASM faster
convergence is necessary.
