  We prove limit theorems and variance estimates for quantities related to
ponds and outlets for 2D invasion percolation. We first exhibit several
properties of a sequence $({\mathbf{O}}(n))$ of outlet variables, the $n$th of
which gives the number of outlets in the box centered at the origin of side
length $2^n$. The most important of these properties describes the sequence's
renewal structure and exponentially fast mixing behavior. We use these to prove
a central limit theorem and strong law of large numbers for
$({\mathbf{O}}(n))$. We then show consequences of these limit theorems for the
pond radii and outlet weights.
