  We consider dense graph sequences that converge to a connected graphon and
prove that the GHP scaling limit of their uniform spanning trees is Aldous'
Brownian CRT. Furthermore, we are able to extract the precise scaling constant
from the limiting graphon. As an example, we can apply this to the scaling
limit of the uniform spanning trees of the Erd\"os-R\'enyi sequence
$(G(n,p))_{n \geq 1}$ for any fixed $p \in (0,1]$, and sequences of dense
expanders. A consequence of GHP convergence is that several associated
quantities of the spanning trees also converge, such as the height, diameter
and law of a simple random walk.
