regime* of our dynamics, i.e., the regime where $(\boxminus,\boxplus)$ is a *metastable pair* in the sense of [@BdH15 Chapter 8].

[**2.**]{} The scaling behaviour of $\Gamma_n^\star$ as $n\to\infty$, as well as the geometry of ${\mathcal{C}}_n^\star$ are hard to capture. We can only offer some conjectures.

\[conj:scalnucltime\] There exists a $\gamma^\star \in (0,\infty)$ such that $$\lim_{n\to\infty} {\mathbb{P}}_n\Big( \big| n^{-1} \Gamma^\star_n - \gamma^\star\big|
> \delta\Big) = 0 \qquad \forall\,\delta>0.$$

\[conj:scalcritdrop\] There exists a $c^\star \in (0,1)$ such that $$\lim_{n\to\infty} {\mathbb{P}}_n\Big( \big| n^{-1} \log|{\mathcal{C}}^\star_n| - c^\star\big|
> \delta\Big) = 0 \qquad \forall\,\delta>0.$$

\[conj:scalprefac\] There exists a $\kappa^\star \in (1,\infty)$ such that $$\lim_{n\to\infty} {\mathbb{P}}_n\Big( \big| |{\mathcal{C}}^\star_n|\,K^\star_n - \kappa^\star\big|
> \delta\Big) = 0 \qquad \forall\,\delta>0.$$

As is clear from the results mentioned in Section \[literature\], all three conjectures are true for the torus, the hypercube and the complete graph. This supports our belief that they should be true for a large class of random graphs as well.

[**3.**]{} In Section \[CMdynamic\] we will give a *dynamical construction* of ${\mathrm{CM}}_n$ in which vertices are added one at a time and edges are relocated. This leads to a *random graph process* $({\mathrm{CM}}_n)_{n\in{\mathbb{N}}}$ whose marginals respect the law of the Configuration Model. In Section \[tailprop\] we will show 