  Let $B_n$ be the poset generated by the subsets of $[n]$ with the inclusion
as relation and let $P$ be a finite poset. We want to embed $P$ into $B_n$ as
many times as possible such that the subsets in different copies are
incomparable. The maximum number of such embeddings is asymptotically
determined for all finite posets $P$ as $\frac{{n \choose \lfloor
n/2\rfloor}}{M(P)}$, where $M(P)$ denotes the minimal size of the convex hull
of a copy of $P$. We discuss both weak and strong (induced) embeddings.
