Packing degenerate graphs

Given $D$ and $\gamma >0$, whenever $c>0$ is sufficiently small and $n$ sufficiently large, if $\mathcal{G}$ is a family of $D$-degenerate graphs of individual orders at most $n$, maximum degrees at most $\frac{cn}{\log n}$, and total number of edges at most $(1-\gamma )\left(\genfrac{}{}{0px}{}{n}{2}\right)$, then $\mathcal{G}$ packs into the complete graph $K_n$. Our proof proceeds by analysing a natural random greedy packing algorithm. This version of the manuscript corrects a small error that appeared in the published version [Adv Math, 354 (2019), 106739].