On the fractal characteristics of the η model

Since the η or dielectric breakdown model was proposed, it has been generally accepted that the fractal characteristics of the so-grown clusters have a smooth behavior as η increases from 0 to infinity. On the basis of recent theoretical calculations on a related model, we conjecture that the aggregate can become effectively branchless for η larger than a critical value η1. A related possibility is that the value 1 for the fractal dimension might be reached at finite values of η. We have carried out a large simulation program to test these conjectures and we find evidence supporting their validity. This is a preliminary report of our work on this problem.