The magnetization of three different systems of diluted easy-axis antiferromagnets, Mn1-xZnxF2, K2Fe1-xInxCl5.H2O and Rb2Fe1-xInxCl5.H2O, reveals that a remanent magnetization, Mr, developes below the Néel temperature. The remanent magnetization is observed when fields as low as 10-3 Oe are applied parallel to the easy axis. At a given temperature, Mr increases with Haxial but is practically saturated in fields as low as a few Oe. The normalized remanent magnetization Mr(t)/Mr(0) is an universal function of the reduced temperature t = T/TN. The function is the same for all three site-diluted systems and is independent of x and Haxial. The origin of Mr is still not known with certainty, but several experimental results suggest the formation of a domain structure, possibly with magnetization in the domain walls. The possibility of the piezomagnetic effect as the origin of Mr, as suggested by other authors, is excluded on the basis of symmetry arguments and the observed magnetic structures of K2FeCl5.D2O and Rb2FeCl5.D2O.