In a previous study of the effects of cooling and solidification on flows issuing onto a horizontal plane and spreading under gravity we considered the case of a viscous fluid that solidifies to form a thin surface crust with a finite yield strength. In that case, the coupling of solidification and viscous stresses in the flow led to a sequence of flow regimes or styles of flow and crustal deformation. Here, we study the spreading, from a small source, of a plastic material having a yield strength before cooling. In this case the fluid again begins to freeze as it spreads radially under gravity, and forms a dome having a surface crust which is stronger than the extruded fluid. If cooling is sufficiently rapid compared to gravity-driven spreading, the flow is found to be controlled by solidification. The flow again takes on one of a number of flow regimes depending on the pace of solidification relative to the rate of lateral flow, or extrusion rate. However, these flow regimes are quite different from those for the viscous extrusions, implying that the internal yield stress has a strong influence on the behaviour. Styles of flow ranged from inflation of an axisymmetric dome to irregular extrusion of lateral lobes and vertical spines. These qualitatively different regimes have much in common with the eruption styles of volcanic lava domes produced by effusion of extremely viscous silicic magmas which may possess a yield strength, and the model provides information about the factors influencing the morphology and hazards of such volcanic flows.