We study the number of in-branch subsets M(m) on a two-dimensional off-lattice diffusion-limited aggregation simulation, where m is the number of particles of an m-branch. The M(m) decays exponentially, however, for small m its behavior is not simple. The probability distribution of each length subset P(m) = M(m)/M-all is independent of cluster size, where M-all = Sigma(m) M(m). The mean branch length (L) over bar approximate to2.34 is found from the above distribution. The P(m) is represented by a branching dynamic model (BDM) including only S(tip)approximate to0.785 which is the tip-sticking probability of a Brownian particle. Moreover, (L) over bar approximate to2.34 is related to S(tip)approximate to0.785. Therefore, we understand that the branching distribution is decided only by the tip-sticking probability. (C) 2002 Elsevier Science B.V. All rights reserved.