We present a theoretical description of linker-mediated self-assembly of gold nanoparticles (Au-NP). Using mesoscale simulations with a coarse-grained model for the Au NPs and dirhenium-based linker molecules, we investigate the conditions under which large clusters can grow and construct a phase diagram that identifies favorable growth conditions in terms of floating and bound linker concentrations. The findings can be considered as generic, as we expect other NP-linker systems to behave in a qualitatively similar way. In particular, we also discuss the case of antibody-functionalised Au NPs connected by the C-reactive proteins (CRPs). We extract some general rules for NP linking that may aid the production of size- and shape-specific NP clusters for technology applications.