This question was put to me by a friend of mine (no, not the one with all the anti-Mormon questions). The answer is a “not really…well, sort of, I guess…well, I guess I can see why people would say that” type of answer.
The quick answer is “No, we believe we get an entire universe” but even that would be misleading because the real answer is “We don’t know.” Allow me to explain, and prepare for your eyebrows to raise a little. Here it is in a nutshell.
Mormons believe that human beings are children of God, and as such, have within them the potential to become like God. Got it? Let me say it more clearly. We believe that we can become Gods. Trust me, if you think about it and read the Bible from this perspective a lot of things will start to make sense. Just read Romans 8 where Paul says that we’re children of God and that we’re joint-heirs of God with Jesus Christ. In other words Christ is our brother and together with him we’re all heirs to what God has. What does God have? The kind of life a God lives. Here’s shocker #2–we believe God used to be a man, just like us.
Now this brings up all sorts of logical and reasonable questions like “When did Gods begin then?” and “Is God the God of the entire universe or just part of it or are there other universes?” and “So there are other Gods then?” and the answer to all of these and many other questions is “We don’t know.” All we worry about is one God.
But one of the questions that arises is “So what is God all about, and if we’re going to be like him then what do we go about doing after we die?” and the logical answer would be that if we become like God then we would create other planets like this one and populate them with our children, just like God has done with this one. And I’m guessing that’s where people would come up with the idea that Mormons believe they get a planet when they die. But as for me, I’m holding out for my own universe, although I’m sure it requires a bit of after-death training to run one.