We study the influence of different magnetic boundary conditions on the gen
eration of magnetic fields by turbulent convection. It is found that the st
ructure and strength of the generated field in the vicinity of the boundary
is strongly dependent on the choice of boundary conditions. In the convect
ive interior, however, the solutions remain largely insensitive to the boun
dary conditions. In all cases the overall efficiency of the dynamo process
remains high with a steady state magnetic energy density between 12 and 25
per cent of the turbulent kinetic energy, and peak field values exceeding t
he equipartition level. These results support the idea that the solar granu
lation may constitute a dynamo source for magnetic fields in the quiet phot
osphere.