Metal flux at consuming interfaces (e.g., sensors or microorganisms) is simulated in environmental multiligand systems using a new numerical code, MHEDYN (Multispecies HEterogeneous DYNamics), based on the lattice Boltzmann method. The attention is focused on the computation of the maximum flux of Cu(II), that is, the flux controlled by diffusion-reaction in solution, irrespective of processes occurring at the interface. In parts III and IV of this series, three types of typical environmental complexants are studied: (a) simple ligands (OH- and C03(2-)), (b) fulvic or humic substances including many sites with broadly varying rate constants, and (c) aggregates including a broad range of sizes and diffusion coefficients. Part III focuses on computations in the presence of simple ligands and fulvic/humic substances separately, and part IV discusses the case of aggregate complexes alone and the mixtures of all ligands in typical natural waters. These papers describe the dynamic contribution of the various types of sites for fulvic and aggregate Cu(II) complexes for the first time. Whenever possible, the metal fluxes computed by MHEDYN are compared with those given by another code, FLUXY, based on a fully different mathematical approach, and very good agreement between these codes is obtained. In all cases, MHEDYN computes the concentration profile of each complex and its time evolution, as well as the steady-state flux and the corresponding contribution of each complex to the flux. The metal fluxes can be computed at a planar consuming surface such as an organism or a sensor surface, in presence of an unlimited number of complexation reactions of the metal M, and for any metal/ligand concentration ratio, with values of the physicochemical parameters ranging over many orders of magnitude.