  We consider a model of $n$ non-intersecting squared Bessel processes with one
starting point $a>0$ at time t=0 and one ending point $b>0$ at time $t=T$.
After proper scaling, the paths fill out a region in the $tx$-plane. Depending
on the value of the product $ab$ the region may come to the hard edge at 0, or
not. We formulate a vector equilibrium problem for this model, which is defined
for three measures, with upper constraints on the first and third measures and
an external field on the second measure. It is shown that the limiting mean
distribution of the paths at time $t$ is given by the second component of the
vector that minimizes this vector equilibrium problem. The proof is based on a
steepest descent analysis for a $4 \times 4$ matrix valued Riemann-Hilbert
problem which characterizes the correlation kernel of the paths at time $t$. We
also discuss the precise locations of the phase transitions.
