As far as I can determine, no one has ever mentioned or written about the 3 types of partials. One of them is commonly used. One is rare and the third is very rare.
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The most common partial, found on toy train and hi-rail layouts alike, is when a road, tracks, river, mountain, forest, etc etc ends abruptly at the train table edge. Your mind naturally fills in the missing pieces just like when you are reading a good novel. You imagine things happening that are not there, such as the mountain chain continuing for several hundred more miles, the river running to the sea eventually, and the road or track leading off somewhere distant.
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This partial is a bit rare but nevertheless is used on occasion. It consists of splitting a building at the table edge so you can see inside the building. Spankybird did this with a circus tent. The same could be done by splitting a train in two, such as a passenger train and the locomotive, but this train splitting idea has never been done before, probably because the thought of slicing a train in half lengthwise is too grotesque to ponder.
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This last partial is EXTREMELY rare. It consists of adding a complete structure such as a building or oil storage tank near the edge of the layout with the deception being that it continues just off the table. This is esp. useful for extremely large structures that simply won’t fit on your layout. Some examples might be a weighing station on a spur leading to a coal unloading operation. You don’t have room for the entire coal structures, coal piles and stuff like that, except for perhaps a small pile of coal. But, this gives you an excuse to run a coal drag. An example for a grain elevator or steel mill could also be devised, where the hint of bigger things could be made by putting some structures or stuff near the edge of the layout that you would recognize. Stuff you might recognize for example would be steam locomotive spare parts at the edge of a turntable, with partial tracks leading to a roundhous
