The effects of unsaturation (including the C-C double bond's position in the alkyl chain) and the ester moiety in the fuel molecule on the morphology of soot particles in a laminar coflow diffusion flame are studied. The effects of the ester moiety are evaluated by comparing an n-decane flame with a biodiesel surrogate flame (composed of 50%/50% molar blend of n-decane and methyl octanoate). The effects of the unsaturation and the position of C-C double bond in the alkyl chain are analysed by comparing 1-decene, 5-decene and n-decane flames. Particles were collected thermophoretically on Transmission Electron Microscopy (TEM) carbon coated copper grids. TEM images are analysed to obtain parameters related to the size of the agglomerates such as radius of gyration, and morphological parameters such as fractal dimension and prefactor of the power-law relationship. The results show that the average primary particle diameter, the size of the agglomerates and the number of primary particles composing the agglomerates increase along the flame length to around two thirds of the flame length and then decrease as a consequence of oxidation becoming dominant over soot nucleation and growth. The fractal dimension of the agglomerates does not change significantly along the different pathlines of the flames. However, effects of the fuel chemical structure are clear. The lowest fractal dimensions are observed for the oxygenated fuel and the highest ones for the unsaturated fuels, with higher fractal dimension when the double bond is located at the edge of the molecule. The same trends are observed for agglomerate sizes: smallest agglomerates are observed for the oxygenated fuel and largest ones for the unsaturated fuels. This suggests that low soot-emitting fuels reduce their size as a consequence of oxidation while keeping their agglomeration skeletal structure.