Let A be a finite dimensional hereditary algebra over an algebraically closed field k, and let A~((m))be the m-replicated algebra of A. In this paper, we investigate the structure properties of the endomorphism algebras of tilting modules of A~((m)), and prove that all the endomorphism algebras of tilting modules of can be realized as the iterated endomorphism algebras of BB-tilting modules. That is, for each pair of basic tilting A~((m))-modules T_1 and T_2 there exists a series of finite dimensional algebras Λ_0,Λ_1,...,Λ_s, which are the endomorphism algebras of some basic tilting A~((m))-modules, and for each Λ_i there is a BB-tilting Λ_i-module M_i such that Λ_0 = End_(A(m)) T_1, A_i = End_(Λi-1) M_(i-1) for 1 ≤ i ≤ s, and End_(A(m)) T2 approx. = EndΛ_s M_s.
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