[tialaramex]

Southern has a bunch of different variants of class 377 in different lengths, so presumably your 12 cars would have been 3 x 4 car length 377s.

Depending on what they had spare ("due to a fault") the 10 cars might have consisted on 2 x 3 car plus 1 x 4 car, or of 2 x 5 car configurations.

In the latter case obviously the train can't split three ways, that's impossible. I would expect that for your service they would choose to run the train to Brighton, then split it and run half to Southampton Central, half to Bognor.

To be fair this route actually could be served (albeit with a little delay) by a single train, there's no huge divergence along the route to serve all of them, it's mostly that it'd be a pain to get back out of Bognor heading for Southampton, the signaller may not want to allow the relevant movement (crossing from the up to the down side, or reversing on the down side) and the driver may not be trained to do it even if a signaller will signal it.