  In this paper we prove that the center of mass of a supercritical
branching-Brownian motion, or that of a supercritical super-Brownian motion
tends to a limiting position almost surely, which, in a sense complements a
result of Tribe on the final behavior of a critical super-Brownian motion. This
is shown to be true also for a model where branching Brownian motion is
modified by attraction/repulsion between particles.
  We then put this observation together with the description of the interacting
system as viewed from its center of mass, and get the following asymptotic
behavior: the system asymptotically becomes a branching Ornstein Uhlenbeck
process (inward for attraction and outward for repulsion), but the origin is
shifted to a random point which has normal distribution, and the Ornstein
Uhlenbeck particles are not independent but constitute a system with a degree
of freedom which is less by their number by precisely one.
