  We consider a single species reaction diffusion system on a two dimensional
lattice where the particles $A$ are biased to move towards their nearest
neighbours and annihilate as they meet; $A + A \to \emptyset$. Allowing the
bias to take both negative and positive values parametrically, any nonzero bias
is seen to drastically affect the behaviour of the system compared to the
unbiased (simple diffusive) case. For positive bias, a finite number of dimers,
which are isolated pairs of particles occurring as nearest neighbours, exist
while for negative bias, a finite density of particles survive. Both the
quantities vanish in a power law manner close to the diffusive limit with
different exponents. In addition, a discontinuity is observed at the fully
positive bias limit. The persistence behaviour is also analysed for the system.
