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For a graph $H$, let $$c_{\infty}(H)= \lim_{n \to\infty}\max\frac{|E(G)|}{n},$$ where the maximum is taken over all graphs $G$on $n$ vertices not containing $H$ as a minor. Thus $c_{\infty}(H)$ is theasymptotic maximum density of graphs not containing $H$ as a minor. Employing astructural lemma due to Eppstein, we prove new upper bounds on $c_{\infty}(H)$for disconnected graphs $H$. In particular, we determine $c_{\infty}(H)$whenever $H$ is union of cycles. Finally, we investigate the behaviour of$c_\infty(sK_r)$ for fixed $r$, where $sK_r$ denotes the union of $s$ disjointcopies of the complete graph on $r$ vertices. Improving on a result ofThomason, we show that $$c_\infty(sK_r)=s(r-1)-1 \mathrm{\; for \;} s={\Omega}\left(\frac{\log{r}}{\log\log{r}}\right),$$ and$$c_\infty(sK_r)>s(r-1)-1 \mathrm{\; for \;} s={o}\left(\frac{\log{r}}{\log\log{r}}\right).$$

Asymptotic Density of Graphs Excluding Disconnected Minors