ḵšathrá refers to the boundlessness of god-beings verses the limitation of men. ḵšathrá is the unlimited, prolific, inexhaustible god-power to make the realm bountiful (See Yasna 28.3, 2nd rhymed verse line and Yasna 31.4, 3rd rhymed verse line.)
ḵšathrá comes from ḵši and the reconstructed Indo European root *tkeh 1- “to rule, bring land into cultivation/bloom.” This ancient sense of “making earth bloom” is present for example in the poetic gathas Yasna 48.11, 2nd rhymed verse line and Yasna 29.2, 2nd rhymed verse line. Greek krasthai “to acquire, possess to cultivate” comes from the same root.
In the ancient commentaries of the poetic gathas ḵšathrá is equated with ḵüdáyî or khüdáyî “god-hood, god-power” from ḵva-tava, Vedic sva-tava “masterly, competent, clever, thriving by own self.”
(See Yasna 31.21, 2nd rhymed verse line ḵva-paithyát, “be ruler, master by own self” from pótis)
The Persian word for god or khuda comes from the same root. The remarkable idea here is that godhood is equated with skillfulness, industry, innovation and cultivation NOT despotism.
In the Achaemenid texts for example we read:
baga vazraka ahuramazdā “a vigorous, robust god is Ahuramazda’. Vazraka (vigorous, robust is also applied to the ruler/king: ḵšāyaθiya vazraka, and vazraka (vigor, health) is also applied to the “land, earth” bumi.
*vazra-, from the root *vaz– ‘be vigorous, strong, full of vigor’ (cf. Lat. vegeo), corresponds to Vedic vāja. (See Benveniste)
However, scholars such as Calvert Watkins and Didier Calin more convincingly argue that the correct root is wag “split, break open, bloom.” (Compare Tocharian wāk “split, bloom” and Hittite wāki “cut into something”)
Ahuramazda is defined as vazraka, this is because godhood is identified with the vigorous life-force. The ruler of the realm is also endowed with vigorous power vazraka, to make the land bloom and the realm bountiful. Likewise the earth as the prototype of fertility and bountifulness bears this epithet.
In the poetic gathas, ḵšathrá is the dominion, realm of health, vigor and wellness haûrvatátö (See Yasna 34.1, 2nd rhymed verse line and Yasna 45.10, 4th rhymed verse line.
ḵšathrá also comes with vôhü “goodness,” for godhood is all goodness, giver of boons and wonders. (See Yasna 31.22, 2nd rhymed verse line, Yasna 41.2 and Yasna 51.1, 1st rhymed verse line.)
The beginning words of Yasna 51.1, 1st rhymed verse line of the poetic gathas are Vôhü ḵšathrem vairîm “the good or wondrous realm of will power.”
In Mazdean wisdom; the dominion of god-beings is a wondrous realm wherein mortals can overcome their limitations, aspire to ideals and realize the triumph of their will power vairîm.
(ḵšathrem vairîm has become shahrivar in Persian.)