Scattered Across Time and Space

Objects or people are sent to not one, but many separate places in time at once. This is often done by result of an accident involving or untrained use of time travel stuff, but can occur due to a time-traveling antagonist hiding objects at various exotic areas (reasons they aren't still there in the present optional) that the time-travelling heroes must locate. This is naturally an excuse for a work to travel to wherever and more importantly whenever the creators deem interesting enough to set some of the work.

Since it involves multiple objects to find and the continued existence of these objects in the past is often hazardous due to risk of Temporal Paradox or leaving a villain free to meddle with history, it naturally pairs with Gotta Catch Them All.

Fan Works

 * In the RWBY fanfic Emergence, the members of Team RWBY arrive on Earth over the course of several weeks, in locations all over the globe, despite all being affected by the same event. Averted with Team JNPR, who all arrive together in Washington, DC as the result of a different incident a year or so later; Cinder, Mercury and Emerald, transported in the same incident, also stay together, but arrive at a different location and time from JNPR.

Live-Action TV

 * Season 2 of DC's Legends of Tomorrow opens with the cast having been stranded in various time periods ranging from the Cretaceous onward due to use of the emergency Time Scatter functionality.

Video Games

 * Where in Time Is Carmen Sandiego? has Carmen deposit her crew throughout time to steal historical artifacts. Now ACME must track her crew down and recover the stolen objects.
 * TimeSplitters 2 has the TimeSplitters take the time crystals to various points of history to hide them from the protagonists.
 * Recovering people, creatures and objects from the past and present of the Wizarding World that have been fragmented and scattered through the Muggle world was the primary goal and gameplay loop in the now-defunct Augmented Reality Game Harry Potter: Wizards Unite
 * Ape Escape starts with monkeys activating a time machine and being scattered throughout history to rewrite the past and become the dominant species on Earth.