Supercritical site percolation on the hypercube: small components are small.

We consider supercritical site percolation on the $d$ -dimensional hypercube $Q^d$. We show that typically all components in the percolated hypercube, besides the giant, are of size $O(d)$. This resolves a conjecture of Bollobás, Kohayakawa, and Łuczak from 1994. [ABSTRACT FROM AUTHOR]