Pavez-Signé's spanning subdivision conjecture

Let $H$ be a graph with $m$ edges and no isolated vertices. Let $\varepsilon>0$ and let $C_0$ be a positive constant depending on $H$ and $\varepsilon$.

Pavez-Signé's conjecture. For all $C\geq C_0$ and any integer $m$, if $G$ is a graph on $n\geq Cm$ vertices with minimum degree at least $(1/2+\varepsilon)n$, then $G$ contains a spanning $H$-subdivision.

This conjecture was raised by Pavez-Signé and is settled in the source paper in a stronger form for digraphs with minimum in- and out-degree at least $n/2$.