  We use Monte Carlo methods to study spinons in two-dimensional quantum spin
systems, characterizing their intrinsic size $\lambda$ and confinement length
$\Lambda$. We confirm that spinons are deconfined, $\Lambda \to \infty$ and
$\lambda$ finite, in a resonating valence-bond spin-liquid state. In a
valence-bond solid, we find finite $\lambda$ and $\Lambda$, with $\lambda$ of a
single spinon significantly larger than the bound-state---the spinon is soft
and shrinks as the bound state is formed. Both $\lambda$ and $\Lambda$ diverge
upon approaching the critical point separating valence-bond solid and N\'eel
ground states. We conclude that the spinon deconfinement is marginal in the
lowest-energy state in the spin-1 sector, due to weak attractive spinon
interactions. Deconfinement in the vicinity of the critical point should occur
at higher energies.
