The elemental composition of the Sun III. The heavy elements Cu to Th

We re-evaluate the abundances of the elements in the Sun from copper ($Z=29$) to thorium ($Z=90$). Our results are mostly based on neutral and singly-ionised lines in the solar spectrum. We use the latest 3D hydrodynamic solar model atmosphere, and in a few cases also correct for departures from local thermodynamic equilibrium (LTE) using non-LTE (NLTE) calculations performed in 1D. In order to minimise statistical and systematic uncertainties, we make stringent line selections, employ the highest-quality observational data and carefully assess oscillator strengths, hyperfine constants and isotopic separations available in the literature, for every line included in our analysis. Our results are typically in good agreement with the abundances in the most pristine meteorites, but there are some interesting exceptions. This analysis constitutes both a full exposition and a slight update of the relevant parts of the preliminary results we presented in Asplund, Grevesse, Sauval & Scott (arXiv:0909.0948), including full line lists and details of all input data that we have employed.