The nonzero widths of heavy particles become significant when they appear in the final state of any decay occurring just around its kinematical threshold. To take into account such effects, a procedure, called the convolution method, was proposed by Altarelli, Conti, and Lubicz. We expand their study which included only threshold effects for t -> bWZ in the standard model. We discuss finite width effects in the three-body decays t -> cWW,cZZ and A(0)(h(0))-> tbW in the type III version of a two-Higgs doublet model. In particular, we find a substantial enhancement in the decay t -> cZZ, which brings its branching ratio to BR(t -> cZZ)similar to 10(-3), and in the decay A(0)-> tbW, which, unlike the h(0) case, becomes competitive with the A(0) two-body decay modes.