  We find that 2-dimensional (2-D) critical branched polymers with no
impurities conclusively belong to the same universality class as 2-D random
percolation clusters, although pure critical 3-D branched polymers do not
belong to the 3-D percolation universality class. We find, moreover, that the
fractal dimension of critical branched polymers in 2-D is independent of the
presence of a random environment, and explore possible explanations for these
strange results. We also report that when there are no impurities the critical
branching probability in 3-D is bc=3.34e-4 +- 0.16e-4.

Statistical Mechanics