H(n)-factors in random graphs

For graphs Gn on n vertices and H(n) on hn vertices, where hn divides n, an H(n)-factor of Gn is a spanning subgraph of Gn consisting of n/hn vertex disjoint copies of H(n). Our main result has supplied a lower bound (or upper bound) of p in the problem of determining the minimal (or maximal) probability p=p(n), for which almost surely random graph G(n;p) contains an (or contains no) H(n)-factor, where H(n) satisfies certain conditions. The bound of p for the same problem when H(n) is a fixed graph has been studied by Alon and Yuster and by Ruciński and by Krivelevich.