  The effect of blocking between different species occurring in one dimension
is investigated here numerically in the case of particles following branching
and annihilating random walk with two offsprings. It is shown that
two-dimensional simulations confirm the field theoretical results with
logarithmic corrections. In one dimension, however, if particles exhibit hard
core interaction I confirm the very recent predictions of Kwon et al. [PRL {\bf
85}, 1682 (2000)] that there are two different universality classes depending
on the spatial symmetry of the offspring production characterized by
$\beta_S=0.5$ and $\beta_A=2$. Elaborate analysis of simulation data shows that
the order parameter exponent $\beta$ does not depend on initial conditions or
on diffusion rates of species but strong correction to scaling is observed. By
systematic numerical simulations the critical point properties have been
explored and initial condition dependence of the dynamical exponents $Z$ and
$\alpha$ is shown. In the case of a random initial state the particle-density
decay at the critical point follows the $t^{-1/4}$ law with logarithmic
corrections.
