The morphology of deposits on $15-{mu}m$ thin SiC filaments has been investigated with SEM in a co-flowing, propane/air laminar diffusion flame. The average size of mature soot particles deposited in the luminous flame edge is strongly dependent on their axial position in a typical heavily sooting flame. The surface growth of liquid-phase PAHs molecules and the transition to soots from fully-developed precursors could be observed in the radial deposition of the flame. Two sooting regimes were found: one is the transition from the condensed-phase precursors; the other is the aggregation of smaller soot particles (or chains of them) to be carried along particle path lines. In the high temperature flame edge outside the soot luminous flame surface, the very thin fiber-like structures, which are about 10 nm thick, were found.