The equilibrium morphology of the nematic (N) - smectic B (SmB) interface, and its growth properties have been studied in quasi-twodimensional geometry. After thermal equilibration at the N - SmB phase transition temperature T-NS two different equilibrium shapes of the SmB phase were found, depending on its orientation. The surface tension anisotropy has been determined from the shape anisotropy of the smectic body. An interesting "inverse process" has been detected in melting of the rapidly grown smectic phase. The stable nematic phase nucleated substancially below T-NS. Most of these nematic germs had uniform oval shape, totally different from that of the equilibrium smectic seed. The morphology of the growing smectic B phase in a supercooled nematic also has been studied. Different morphologies were observed, depending on the substance, undercooling Delta T = T-NS - T, and alignment of the growing SmB germ. In order to compare the growth dynamics, the area of the patterns was measured and the square root of it versus time was plotted.