In high-temperature gas-cooled reactors (HTGRs), carbonaceous dust can be generated both during normal operations and during accidents. The dust particles can be highly irregular and highly porous and have very large surface areas that may make dust-facilitated (or dust-hindered) fission product (FP) transport a major factor. Since the FP interactions with dust can occur while the dust is on a surface as well as in suspension, there is a need to obtain computational and experimental results for both situations. In 2014, Smith and Loyalka used the Green's Function Method to study condensation (results for absorption/deposition and evaporation are generally directly related to the condensation problem) on chainlike particles and particle agglomerates in the diffusion regime. In 2010, Smith and Loyalka made progress in computation of evaporation/condensation particles on a surface, but again in the diffusion regime. Since the particle sizes of interest span a wide range—from nanometers to microns (10−9 m to 10−6 m)—and are also porous with small pores and pathways for FPs, these computations need to be extended to the transport regime where the particle sizes (and/or pores) are comparable to the vapor (FP) molecular mean free path (∼0.05 μm) in the gaseous phase (air or helium, or some mix thereof with other contaminants). The focus of the present paper is on Monte Carlo computation of condensation rate on chainlike particles and particle agglomerates in the transport regime using the one-speed approximation, and we report a number of new results that provide new insights and path for future explorations.