  This is an expository note answering a question posed to us by Richard
Stanley, in which we prove a limit shape theorem for partitions of $n$ which
maximize the number of subpartitions. The limit shape and the growth rate of
the number of subpartitions are explicit. The key ideas are to use large
deviations estimates for random walks, together with convex analysis and the
Hardy-Ramanujan asymptotics. Our limit shape coincides with Vershik's limit
shape for uniform random partitions.
