Here's what I found about 'universal dominion'.
http://biblehub.com/sermons/auth/mci..._of_christ.htm
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Matthew 28:18
And Jesus came and spoke to them, saying, All power is given to me in heaven and in earth.
I. THE UNIVERSAL DOMINION OF CHRIST HERE ASSERTED — "All power," etc. The word "power" in our language is ambiguous. Sometimes it signifies ability or capacity, and sometimes rightful authority. In both these senses it is true of Christ; He has both the ability to act and the authority to warrant His acting.
1. That as a Divine Person the Saviour has all power inherent in Himself.
2. In virtue of office, the power here spoken of is delegated to Christ — "All power is given," etc.
3. This power and authority extend to universal nature.
4. This power is deposited in Christ as the Head of the Church, and to be exercised for her benefit.
5. This power is to be exercised in the destruction of all who do not submit to it.
II. THE COMMISSION GIVEN BY CHRIST TO HIS MINISTERS IN VIRTUE OF THAT POWER WITH WHICH HE IS INVESTED.
1. That it is only to those who are called by God, and qualified for His service, that this commission is given.
2. This commission extends to all nations as regards the persons to be benefited by it.
3. It embraces all that the Saviour has made known in His word.
III. To CONSIDER THE ENCOURAGEMENTS AFFORDED TO THE AMBASSADORS OF CHRIST IN THE DISCHARGE OF THEIR DUTY.
1. Christ is with His Church and people always; not His essential but gracious presence.
2. A particular call to notice this truth, "I am with you always." How highly is Jesus exalted.
(R. McIndoe.)"
http://www.lcoggt.org/Riggle/ch27.htm
"The Saints Will Have Universal Dominion.
The final triumph of Christianity over all other religions and faiths is assured in the Word of God. In
Daniel 2 we read of a “stone cut out without hands.” This refers chiefly to the church or kingdom of God—Christianity. It did not come by human hands. Being divine, it came from heaven. It is of a spiritual nature; hence no worldly policy, human doctrine, nor military force was employed in its establishment. “Not by might nor power, but by the Spirit of the Lord of hosts.” This stone smote the image and broke it to pieces. As observed in a previous chapter, the great image represented four heathen kingdoms that reigned in succession in ancient times. These were the Babylonian, the Medo-Persian, the Grecian, and the Roman. It was the Roman which held the dominion when Christ appeared to set up the everlasting kingdom of heaven. At the time when this heathen government, partaking of all the characteristics of the preceding empire, was at its zenith of imperial splendor, military glory, legislative authority, and literary eminence, Christianity smote it at its very foundation, or principles of support, and by destroying these brought the whole to ruin. This stone began to smite the image when the apostles went out into every part of the Roman empire, pulling down idolatry and founding Christian churches. Soon the saving gospel spread to every quarter. Pagans were converted by the thousands. In A. D. 331, by an edict of the emperor himself, all the heathen temples were ordered destroyed, and Christianity became the religion of the empire. In the very territory where paganism held full sway during the dominion of the Babylonian, Medo-Persian, Grecian, and Roman empires, Christianity was now the universal religion. You see that many of the distinguishing marks and principles of all the preceding empires remained in, and were compacted with, the Roman government, not only as to their territorial possession, but also as to their distinctive characteristics. Thus when Christianity struck at the roots of pagan Rome, not only the iron and clay, but also the brass, the silver, and the gold, representing the former pagan systems and governments, “were broken to pieces together.” Christianity triumphed, and the pagan systems fell.
But mark well the fact that at the very time when Christianity crushed the image and broke it in pieces, it was only “a stone.” That was the blessed morning-light age of the church. Christianity at this time was represented by a stone, and yet that stone filled the Roman empire, or the then-known world; but it was foreseen that this stone which smote the image became a “great mountain and filled the whole earth” (
Daniel 2:34). This shows that the work of Christianity was to be progressive. Beginning small, it was to continue to enlarge and expand. Not only would the Roman empire and a few countries clustering around the Mediterranean Sea be brought under the influence of the gospel, but the kingdom—the church of Christ—would enlarge from a stone into a mountain, yea, “a great mountain, and fill the whole earth.” Wherever it goes, it breaks in pieces, consumes, and destroys idolatry out of the hearts of man.
What was done in the morning-light age of the church throughout the Roman empire is what will be accomplished in the evening light throughout the whole earth. No law or principle in Christianity is directed against the political code of any country, but against the sin and idolatry therein. False religions and corrupt systems of so-called Christianity must give way to pure Christianity revealed in the whole gospel now being preached. That which in primitive times spread out and filled the Roman empire shall in these last days spread from sea to sea and fill the whole earth with its influence. By this I mean that those countries which have not as yet felt the powerful influence of Christianity will yet feel it; for “the earth shall be filled with the knowledge of the glory of the Lord as the waters cover the sea.”
Since the pure and redeemed church of God in this evening time is destined to spread over all the earth, it follows that God’s saints will have the dominion. Not that the temporal governments will be given into their hands, for the reign and kingdom of God is “not of this world.” It is of a spiritual nature. The idea is that in the very nations where paganism and apostate Christianity rule and govern, there pure Christianity will yet wield a mighty influence; and since this triumphant reign is the enjoyment of the saints, who will be distributed in every corner of the earth, theirs is a universal dominion. “He that overcometh and keepeth my words unto the end, to him will I give power over the nations; and he shall rule them with a rod of iron; as the vessels of a potter shall they be broken to pieces.”
Revelation 2:26, 27. The reign of Christ is a spiritual reign, and his kingdom is a spiritual kingdom. He reigns in the hearts of his people.
But his dominion shall be to the ends of the earth. “The uttermost parts of the earth for thy possession”; that is, his truth and kingdom will spread to the uttermost parts of the earth and through its conquering influence will affect every nation. Thus Christianity will become the universal religion of earth. All other religions are of a local nature and apply only to certain nations and peoples, but pure Christianity will apply to all nations, and the prophet said that “all nations shall flow into it.” The universality of Christianity in the earth at the time when Christ comes again, its final and glorious triumph, is clearly seen in many scriptures."