It is a common caricature by anti-Mormons like Ed Decker and James White that the "Mormon God" is only God of this planet or universe. Notwithstanding, this lies in the face of passages in uniquely Latter-day Saint Scriptures, such as:
And worlds without number have I created; and I also created them for mine own purpose; and by the Son I created them, which is mine Only Begotten. (Moses 1:33)
And were it possible that man could number the particles of the earth, yea, millions of earths like this, it would not be a beginning to the number of thy creations; and thy curtains are stretched out still; and yet thou art there, and thy bosom is there; and also thou art just; thou art merciful and kind forever. (Moses 7:30)
And he said unto me: My son, my son (and his hand was stretched out), behold I will show you all these. And he put his hand upon mine eyes, and I saw those things which his hands had made, which were many; and they multiplied before mine eyes, and I could not see the end thereof. (Abraham 3:12)
With reference to the latter two passages, Sidney Sperry wrote the following:
Judging from the information given us by Abraham and by the Prophet Joseph Smith, there are worlds without number and the God whom we worship, the great Elohim, has creations the number of which are beyond the imagination of man. (Sidney B. Sperry, Ancient Records Testify in Papyrus and Stone [Salt Lake City: General Boards of M.I.A. of The Church of Jesus Christ of Latter-day Saints, 1938], 95)
The claim that Latter-day Saint theology teaches that God the Father is only God of this earth or universe is simply false.