Motivated by recent developments in the context of adaptation over networks, this work establishes useful results about the limiting global behavior of diffusion and consensus strategies for the solution of distributed optimization problems. It is known that the choice of combination policies has a direct bearing on the convergence and performance of distributed solutions. This article reveals what aspects of the combination policies determine the nature of the Pareto-optimal solution and how close the distributed solution gets to it. The results suggest useful constructive procedures to control the convergence behavior of distributed strategies and to design effective combination procedures.