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 Neel 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.
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