  We consider a branching particle system where each particle moves as an
independent Brownian motion and breeds at a rate proportional to its distance
from the origin raised to the power $p$, for $p\in[0,2)$. The asymptotic
behaviour of the right-most particle for this system is already known; in this
article we give large deviations probabilities for particles following
"difficult" paths, growth rates along "easy" paths, the total population growth
rate, and we derive the optimal paths which particles must follow to achieve
this growth rate.
