We investigate through direct molecular mechanics calculations the geometrical properties of hydrocarbon mantles subjected to percolation disorder. We show that the structures of mantles generated at the critical percolation point have a fractal dimension df approximately 2.5. In addition, the solvent access surface As and volume Vs of these molecules follow power-law behavior, As approximately L(alphaA) and Vs approximately L(alphaV), where L is the system size, and with both exponents alphaA and alphaV being significantly dependent on the radius of the accessing probing molecule, r(p). Our results from extensive simulations with two distinct microscopic topologies (i.e., square and honeycomb) indicate the consistency of the statistical analysis and confirm the self-similar characteristic of the percolating hydrocarbons. Due to their highly branched topology, this new class of disordered molecules can be of potential use in a variety of practical applications.