  We consider a transmitter broadcasting random linear combinations (over a
field of size $d$) formed from a block of $c$ packets to a collection of $n$
receivers, where the channels between the transmitter and each receiver are
independent erasure channels with reception probabilities $\mathbf{q} =
(q_1,\ldots,q_n)$. We establish several properties of the random delay until
all $n$ receivers have recovered all $c$ packets, denoted $Y_{n:n}^{(c)}$.
First, we provide lower and upper bounds, exact expressions, and a recurrence
for the moments of $Y_{n:n}^{(c)}$. Second, we study the delay per packet
$Y_{n:n}^{(c)}/c$ as a function of $c$, including the asymptotic delay (as $c
\to \infty$), and monotonicity (in $c$) properties of the delay per packet.
Third, we employ extreme value theory to investigate $Y_{n:n}^{(c)}$ as a
function of $n$ (as $n \to \infty$). Several results are new, some results are
extensions of existing results, and some results are proofs of known results
using new (probabilistic) proof techniques.
