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Abstract 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 colourings are close to being $$k$$ -partite, while, for $$c$$ bounded away from $$0$$ , random colourings of an appropriate density are asymptotically optimal and all nearly-extremal colourings are quasirandom. Our investigations also open up a range of questions about what happens for intermediate values of $$c$$ .more » « less
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