Laboratory experiments investigate the radial spread of an intrusion created by a turbulent forced plume in uniformly stratified ambient fluid. The flow evoluti on is determined as it depends upon the ambient buoyancy frequency, N, and the s ource momentum and buoyancy fluxes, M0 and F0, respectively. The plume reaches its maximum vertical extent, Zmax, collapses back upon itself as a fountain and then spreads radially outwards at its neutral buoyancy depth, Zspread, where the intrusion has the same density as the ambient. Through theory and experiments we determine that Zspread=f(sigma) Hp, in which Hp= M0^(3/4) F0^(-1/2), sigma = (M0 N/F0)^2, and f(sigma) propto sigma^(-3/8) for sigma <~ 50 and f(sigma) propto sigma^(-1/4) for sigma >~ 50. In the inertia-buoyancy regime the intrusion front advances in time approximatel y as R propto t^(3/4), consistent with models assuming a constant buoyancy flux into the intrusion. Where the intrusion first forms, at radius R1, its thicknes s h1 is approximately constant in time. The thickness of the intrusion as a who le, h(r,t), adopts a self-similar shape of the form h/h1 ~= [(R-r)/(R-R1)]^p, wi th p ~= 0.55 +/- 0.03. The comparison of these results to large volcanic plumes penetrating into and spreading in the stratosphere are discussed.