  We consider the time-dependent evolution of a relativistic jet following its
breakout through the surface of a massive compact star, as envisaged in the
collapsar model of gamma-ray bursts. At breakout, the jet is tightly collimated
by the pressure of its hot cocoon, which is created as the jet traverses the
star. After breakout, the cocoon pressure drops and the jet expands toward its
natural opening angle. We show that the evolving opening angle of the jet
produces a stratification of the total energy with the off-axis angle,
resulting in a universal morphology. The angular structure is largely
independent of the initial beam pattern and depends only on the luminosity of
the central engine. With the minimal assumption of a constant energy release we
reproduce the theta^{-2} profile required to explain observations of
afterglows.
