  The book graph $B_n^{(k)}$ consists of $n$ copies of $K_{k+1}$ joined along a
common $K_k$. In the prequel to this paper, we studied the diagonal Ramsey
number $r(B_n^{(k)}, B_n^{(k)})$. Here we consider the natural off-diagonal
variant $r(B_{cn}^{(k)}, B_n^{(k)})$ for fixed $c \in (0,1]$. In this more
general setting, we show that an interesting dichotomy emerges: for very small
$c$, a simple $k$-partite construction dictates the Ramsey function and all
nearly-extremal colorings are close to being $k$-partite, while, for $c$
bounded away from $0$, random colorings of an appropriate density are
asymptotically optimal and all nearly-extremal colorings are quasirandom. Our
investigations also open up a range of questions about what happens for
intermediate values of $c$.
