  The displacement of a more viscous fluid by a less viscous one in a quasi-two
dimensional geometry leads to the formation of complex fingering patterns. This
fingering has been characterized by a most unstable wavelength, $\lambda_c$,
which depends on the viscosity difference between the two immiscible fluids and
sets the characteristic width of the fingers. How the finger length grows after
the instability occurs is an equally important, but previously overlooked,
aspect that characterizes the global features of the patterns. As the lower
viscosity fluid is injected, we show that there is a stable inner region where
the outer fluid is completely displaced. The ratio of the finger length to the
radius of this stable region depends only on the viscosity ratio of the fluids
and is decoupled from $\lambda_c$.
