  The paper considers instantly coalescing, or instantly annihilating, systems
of one-dimensional Brownian particles on the real line. Under maximal entrance
laws, the distribution of the particles at a fixed time is shown to be Pfaffian
point processes closely related to the Pfaffian point process describing one
dimensional distribution of real eigenvalues in the real Ginibre ensemble of
random matrices. As an application, an exact large time asymptotic for the
n-point density function for coalescing particles is derived.
