  We investigate the physics of dark matter models featuring composite bound
states carrying a large conserved dark "nucleon" number. The properties of
sufficiently large dark nuclei may obey simple scaling laws, and we find that
this scaling can determine the number distribution of nuclei resulting from Big
Bang Dark Nucleosynthesis. For plausible models of asymmetric dark matter, dark
nuclei of large nucleon number, e.g. > 10^8, may be synthesised, with the
number distribution taking one of two characteristic forms. If
small-nucleon-number fusions are sufficiently fast, the distribution of dark
nuclei takes on a logarithmically-peaked, universal form, independent of many
details of the initial conditions and small-number interactions. In the case of
a substantial bottleneck to nucleosynthesis for small dark nuclei, we find the
surprising result that even larger nuclei, with size >> 10^8, are often finally
synthesised, again with a simple number distribution. We briefly discuss the
constraints arising from the novel dark sector energetics, and the extended set
of (often parametrically light) dark sector states that can occur in complete
models of nuclear dark matter. The physics of the coherent enhancement of
direct detection signals, the nature of the accompanying dark-sector form
factors, and the possible modifications to astrophysical processes are
discussed in detail in a companion paper.
