  We report on some extensive analysis of a recently proposed model [A.
Lipowski Phys. Rev. E {\bf 60}, 6255 (1999)] with infinitely many absorbing
states. By performing extensive Monte Carlo simulations we have determined
critical exponents and show strong evidence that this model is not in the
directed percolation universality class.
  The conjecture that this two-dimensional model exhibits a dimensional
reduction (behaving as one-dimensional directed percolation) is firmly
disproven.
  The reason for the model not exhibiting standard directed percolation scaling
behavior is traced back to the existence of what we call {\it superabsorbing
sites}, i.e. absorbing sites that cannot be directly activated by the presence
of neighboring activity in one or more than one directions.
  Supporting this claim we present two strong evidences: (i) in one dimension,
where superabsorbing sites do not appear at the critical point, the system
behaves as directed percolation, and (ii) in a modified two-dimensional
variation of the model, defined on a honeycomb lattice, for which
superabsorbing sites are very rarely observed, directed percolation behavior is
recovered. Finally, a parallel updating version of the model exhibiting a
nonequilibrium first-order transition is also reported.
