The two splitter trains that I'm sure are still in use are: the Scottish sleeper trains, which split (and combine on the return journey) at Carstairs and Edinburgh; and some Pendolino services from Helsinki which split at Tampere to save traffic slots on the busiest part of the network - but they usually don't join on the return journey, because the couplers are not totally reliable, especially in bad weather. Both of these are very thoroughly intercity services.
Amtrak used to do this on several trains. The Lake Shore Limited had one half come north from New York and the other half west from Boston, and the two halves were combined at Albany for the remainder of the trip to Chicago. It was also known unofficially as the "Late-Fer-Shure Limited", probably because if either half was delayed they had to hold the other half, thus doubling the chances for lateness. They did something similar when they combined the Silver Star with the Silver Meteor, formerly two separate trains, which ran combined from Washington DC to Jax, then split into Tampa- and Miami-bound sections. If I'm reading the current timetable correctly, though, they are two separate trains again.
(This last once had a weird bit wherein each section went over the same piece of track, but in opposite directions: the Tampa section curved first east and then back west, while the Miami section curved west and then back east, like a pair of overlapping parentheses. That was back in the early '90s; it's even weirder now: there's only one train, and it goes south to Lakeland, west to Tampa, and then back east to Lakeland
before proceeding south. WTF?)
Oh, and regarding the London subway map. Anybody remember this version