We use a simple model of the formation, growth, coalescence and migration of veins of basaltic melt generated by partial melting in chondritic asteroids to deduce the sizes of, and pressures within, the fluid-filled dikes reaching the surfaces of such bodies. The gas contents ( 1000 ppm of mainly CO and N2) of the asteroids were high enough that bubbles of free gas trapped in the melt veins gave the basaltic melts significant buoyancy; expansion of these gases as a dike opened to the vacuum at the surface led to fragmentation of the melts into liquid droplets which were transported upwards by the accelerating gases to the surface. The sizes of these droplets and, hence, of the pyroclastic glass beads into which they cooled, are calculated to lie in the range 30 μm to 4 mm; this range is essentially independent of the size or gas content of the asteroid parent and only weakly dependent on the internal pressure of the erupting fluid. The fate of the pyroclasts, however, does depend on all of these factors. At very low internal pressures, significant separation of the gas and liquid in a rising dike may take place and not all of the liquid will be expelled from the dike when it opens to the surface. For relatively large ( 100 km radius) asteroids with relatively low ( 300 ppm) gas contents, the larger clasts are too heavy to be lifted from the level at which magma fragmentation takes place by the gas flow and so would also remain behind to form basaltic veins. The apparent absence of basaltic veins in meteorites then implies both that internal pressures in near-surface dikes were generally greater than 0.3 MPa and that low gas contents were not common. Finally, as long as pyroclasts are lofted from the magma fragmentation level, they will be accelerated to at least 90% of the final gas speed. If this speed exceeds the escape speed from the asteroid (as happens readily for high gas contents and small asteroids), the pyroclasts will be expelled into space and lost from the meteorite record. Otherwise (low gas contents or large asteroids), they will eventually fall back to be incorporated into the surface regolith, modifying the chemical and physical properties of meteorites subsequently derived from it.