2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113549We study the sizes of connected components according to their excesses during a random graph process built with $n$ vertices. The considered model is the continuous one defined in Janson 2000. An ${\ell}$-component is a connected component with ${\ell}$ edges more than vertices. $\ell$ is also called the \textit{excess} of such component. As our main result, we show that when $\ell$ and ${n \over \ell}$ are both large, the expected number of vertices that ever belong to an $\ell$-component is about ${12}^{1/3} {\ell}^{1/3} n^{2/3}$. We also obtain limit theorems for the number of creations of $\ell$-components.A paraître dans AlgorithmicaDiscrete MathematicsCombinatoricsProbabilityG.2.1; G.2.2; G.3text