  We study the one dimensional branching Brownian motion starting at the origin
and investigate the correlation between the rightmost ($X_{\max}\geq 0$) and
leftmost ($X_{\min} \leq 0$) visited sites up to time $t$. At each time step
the existing particles in the system either diffuse (with diffusion constant
$D$), die (with rate $a$) or split into two particles (with rate $b$). We focus
on the regime $b \leq a$ where these two extreme values $X_{\max}$ and
$X_{\min}$ are strongly correlated. We show that at large time $t$, the joint
probability distribution function (PDF) of the two extreme points becomes
stationary $P(X,Y,t \to \infty) \to p(X,Y)$. Our exact results for $p(X,Y)$
demonstrate that the correlation between $X_{\max}$ and $X_{\min}$ is nonzero,
even in the stationary state. From this joint PDF, we compute exactly the
stationary PDF $p(\zeta)$ of the (dimensionless) span $\zeta = {(X_{\max} -
X_{\min})}/{\sqrt{D/b}}$, which is the distance between the rightmost and
leftmost visited sites. This span distribution is characterized by a linear
behavior ${p}(\zeta) \sim \frac{1}{2} \left(1 + \Delta \right) \zeta$ for small
spans, with $\Delta = \left(\frac{a}{b} -1\right)$. In the critical case
($\Delta = 0$) this distribution has a non-trivial power law tail ${p}(\zeta)
\sim 8 \pi \sqrt{3} /\zeta^3$ for large spans. On the other hand, in the
subcritical case ($\Delta > 0$), we show that the span distribution decays
exponentially as ${p}(\zeta) \sim (A^2/2) \zeta \exp \left(-
\sqrt{\Delta}~\zeta\right)$ for large spans, where $A$ is a non-trivial
function of $\Delta$ which we compute exactly. We show that these asymptotic
behaviors carry the signatures of the correlation between $X_{\max}$ and
$X_{\min}$. Finally we verify our results via direct Monte Carlo simulations.
