  We consider exploration algorithms of the random sequential adsorption type
both for homogeneous random graphs and random geometric graphs based on spatial
Poisson processes. At each step, a vertex of the graph becomes active and its
neighboring nodes become explored. Given an initial number of vertices $N$
growing to infinity, we study statistical properties of the proportion of
explored nodes in time using scaling limits. We obtain exact limits for
homogeneous graphs and prove an explicit central limit theorem for the final
proportion of active nodes, known as the \emph{jamming constant}, through a
diffusion approximation for the exploration process. We then focus on bounding
the trajectories of such exploration processes on random geometric graphs, i.e.
random sequential adsorption. As opposed to homogeneous random graphs, these do
not allow for a reduction in dimensionality. Instead we build on a fundamental
relationship between the number of explored nodes and the discovered volume in
the spatial process, and obtain generic bounds: bounds that are independent of
the dimension of space and the detailed shape of the volume associated to the
discovered node. Lastly, we give two trajectorial interpretations of our bounds
by constructing two coupled processes that have the same fluid limits.
