In the context of a Moon race where multiple actors are rushing to get hold of limited resources located in a reduced area, several international fora and working groups have been created to regulate the occupation of these lunar regions and the exploitation of their resources. In the lecture, Tamara Álvarez examines the way in which these regulatory practices are advancing the three-dimensional enclosure of the Moon's land, underground and radiospectrum and setting the basis for a lunar private property regime.