The Shore Leave Planet, also known as the Amusement Park Planet, was an uninhabited planet in the Omicron Delta region. Set up as an amusement park of sorts by an unknown race, as of the late 2260s, it had operated for aeons and served the crews of many ships.
Starfleet first became aware of the planet when the USS Enterprise encountered it in 2267. They found the planet to be lush and beautiful with forests, water, and mountains, – and entirely artificial. The atmosphere was capable of supporting humanoid lifeforms. Constructed by an unidentified race, the planet's idyllic surface concealed a vast factory. Likened to an amusement park, the planet used small antennae to scan the thoughts of visitors. The information thus obtained was used to construct artifacts to implement the fantasies of those visitors; once completed, the artifacts were deposited on the surface, somewhere near the individual whose fantasies they represented.
These artifacts could be almost anything; they ranged from a small 20th century firearm to animals, plants, aircraft, and people. Animated objects, such as people, behaved exactly as their fantasist expected them to behave. Captain Kirk enjoyed a ferocious fight with Finnegan, an old Academy tormentor, and later a rekindled romance with an old flame, Ruth. There was evidence that the artifacts were pre-programmed, and also that the planet could alter their programming after their manufacture; in one case, an existing aircraft strafed two crewmembers immediately after it occurred to one of them that it might take this action. Disabled artifacts, and artifacts whose purpose was ended, disappeared quickly; presumably, they were returned to the underground facility where they had been made.
The artifacts could be dangerous if the fantasy they were part of was dangerous. In two cases, Enterprise crew were seriously injured (at the time, they were believed killed). When this happened, the injured were taken to the complex below, where their injuries were repaired.
The Enterprise crew briefly met one representative of this race, the Keeper, who advised them that his people constructed the planet as a place where they could come, and play. Hikaru Sulu did not believe such an advanced race could possibly need to play, but Kirk opined that "the more complex the mind, the greater the need for the simplicity of play," a statement the Keeper agreed with. The Keeper would not discuss his race, explaining simply that the Federation visitors weren't yet ready to understand them. (TOS: "Shore Leave")
In much need for R&R, the Enterprise visited the planet a second time in 2269. The ship's crew learned that the Keeper, an elderly man at the time they originally met him, had died. They also became embroiled in the schemes of the planetary master computer. This extremely sophisticated intelligence had grown disenchanted with its life of servitude. Charged by its builders with scanning the minds of visitors, and manufacturing their fantasies, it wanted more. To achieve its goals, it imperiled a number of Enterprise crew, and ultimately kidnapped Lieutenant Uhura. After several discussions with her, it eventually embraced a modified worldview, and released the threatened crew members. (TAS: "Once Upon a Planet")
The "planetary effects" were operated by a thought-duplicator master computer capable of reading thoughts, located in a computer center within an underground complex. This complex, which was believed to also contain the Keeper's quarters, was shielded by a solid planetary shell consisting of granite and metal alloy impenetrable by Starfleet sensors. At at least some points, the shell was located barely under the surface.
In the scene descriptions from the final draft script of "Shore Leave", the first view of this planet was described thus; "Park-like... forest and meadows... no structure, people or animals... many flowers... extremely peaceful." The script detailed a glade on the planet's surface as "surpassing anything we've seen thus far."
In the scripted version of his captain's log from "Shore Leave", Kirk described this world as "an uninhabited planet in the Omicron Delta region... earth type... apparently uninhabited...," whereas in the final version of that log entry, he refers to it as "an uninhabited planet in the Omicron Delta region. A planet remarkably like Earth, or how we remember Earth to be. Park-like, beautiful, green, flowers, trees, green lawn, quiet and restful. Almost too good to be true."
An initial Starfleet visit to the Shore Leave Planet was considered for the Star Trek: Enterprise episode "Two Days and Two Nights", but this did not come to pass, due to the planet being new to Starfleet in the episode "Shore Leave"; the planet was ultimately replaced by Risa in the ENT episode. (Star Trek: Communicator issue 143, p. 31)
In the novelization of "Once Upon a Planet", a continuation after the events of the actual episode depicted some of the leisure time spent by Enterprise crew members on the planet. The planet not only featured in that adaptation but also in the novelization of "Mudd's Passion" (which, in Star Trek Log 3, follows "Once Upon a Planet" and was set immediately after it). The latter adaptation referred to the planet upon saying that a party had by the Enterprise's bridge crew (under the influence of love potion crystals) was insisted by some of the celebrators as being even better than their recent stay on the planet.
According to the novel Q&A, this planet is called Beta Omicron Delta III.