Of course this would vary from region to region, but a common answer due to the sparse population and lack of codified rules on the subject basically meant whoever claimed it. This is best seen in Norway after the Plague. Basically what happened was, due tot he devastation of the population, a lot of fertile Land was freed up. This allowed many farmers to expand their lifestyles beyond farming and onto pasturing because they lacked the manpower to farm all that land and meat would get them a pretty good bargain in town, or rather, what was left of the town after the plague.
Source used: Harald Aastorp (1 August 2004). "Svartedauden enda verre enn antatt". Forskning.no
Here's the entry for escheat in Black's Law Dictionary:
escheat (es-cheet), n. (14c) 1. Hist. The reversion of land ownership back to the lord when the immediate tenant dies without heirs. See WRIT OF ESCHEAT. 2. Reversion of property (esp. real property) to the state upon the death of an owner who has neither a will nor any legal heirs. [Cases: Escheat 1–8.] 3. Property that has so reverted. See heirless estate under ESTATE (3). — escheat, vb. — escheatable, adj.
"All escheats, under the English law, are declared to be strictly feudal, and to import the extinction of tenure. . . . The rule [was] that if lands were held in trust and the cestui que trust without heirs, the lands did not escheat to the crown, but the trustee, being in esse and in the legal seisin of the land, took the land discharged of the trust, and bound as owner for the feudal services. But as the feudal tenures do not exist in this country, there are no private persons who succeed to the inheritance by escheat; and the state steps in the place of the feudal lord, by virtue of its sovereignty, as the original and ultimate proprietor of all the lands within its jurisdiction." 4 James Kent, Commentaries on American Law *423–24 (George Comstock ed., 11th ed. 1866).
The implication here being that lands not held in trust escheat (revert) to the crown. The crown likely designated its agent (lord, duke, baron, what have you) to administer the crown's lands. This, by the way , is essentially the system that we still use today, except that instead of the crown we have the state. If you die without a will, there are statutory lines of inheritance and if no relatives at all are available, then the money goes to the state.
This would likely only hold for England and its colonies or areas of influence that use the common law. Most of mainland Europe likely follows a civil or roman code system and I'd be curious to hear from those experiences.