We analyze statistical properties of random walkers which disappear when they meet and make offsprings by a controllable rate. Numerical results for one, two, and three dimensions and for the Sierpinski gasket are assessed in a view of the mean-field theory predictions. Universality classes are found to depend on the number of offsprings in space dimension less than 3.

• Received 28 October 1991

DOI:https://doi.org/10.1103/PhysRevLett.68.3060