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For a fixed bipartite graph H and given number c, 0<c<1, we determine thethreshold T_H(c) which guarantees that any n-vertex graph with at edge densityat least T_H(c) contains $(1-o(1))c/v(H) n$ vertex-disjoint copies of H. In theproof we use a variant of a technique developed byKomlos~\bcolor{[Combinatorica 20 (2000), 203-218}]

The extremal function for partial bipartite tilings