  We examine analytically and numerically the evolution of a relativistic
fireball. We show that, after an early rearrangement phase, most of the matter
and energy in the fireball is concentrated within a narrow shell. The shell
propagates at nearly the speed of light, with a frozen radial profile and
according to a simple set of scaling laws. The spectrum of the escaping
radiation is harder at early times and softer later on. The results are
applicable to models of $\gamma$-ray bursts. Submitted to Monthly Notices of
the RAS Figures available on request from the authors
