Surface-bound exospheres facilitate volatile migration across the surfaces of nearly airless bodies. However, such transport requires that the body can both form and retain an exosphere. To form a sublimation exosphere requires the surface of a body to be sufficiently warm for surface volatiles to sublime; to retain an exosphere, the ballistic escape and photodestruction rates and other loss mechanisms must be sufficiently low. Here we construct a simple free molecular model of exospheres formed by volatile desorption or sublimation. We consider the conditions for forming and retaining exospheres for common volatile species across the Solar System, and explore how three processes (desorption/sublimation, ballistic loss, and photodestruction) shape exospheric dynamics on airless bodies. Our model finds that the CO₂ exosphere of Callisto is much too dense to be sustained by impact-delivered volatiles, but could be maintained by only ~7 ha (~0.07 km²) of exposed CO₂ ice distributed across Callisto (and refreshed through mass wasting). We use our model to predict the peak surface locations of Callisto's CO₂ exosphere along with other Galilean moons, which could be tested by JUICE observations. Our model finds that to maintain Iapetus' two-tone appearance, its dark Cassini Regio likely has unresolved exposures of water ice, perhaps in sub-resolution impact craters, that amount to up to approximately ~0.06% of its surface. In the Uranian system, we find that the CO₂ deposits on Ariel, Umbriel, Titania, and Oberon are unlikely to have been delivered via impacts, but are consistent with both a magnetospheric origin, (as has been previously suggested) or sourced endogenously. We suggest that the leading/trailing CO₂ asymmetries on these moons could result from exosphere-mediated volatile transport, and may be a seasonal equinox feature that could be largely erased by pole-to-pole volatile migration during the Uranian solstices. We calculate that ~2.4–6.4 mm thick layer of CO₂ (depending the moon) could migrate about the surface of Uranus' large moons during a seasonal cycle. Our model also confirms that water migration to Mercury's polar cold traps is inefficient without self-shield against photodestroying UV light, and that Callisto's bright spires could be formed/maintained by exospherically deposited H₂O.