The copyright at the end of TMP does not list Paramount Pictures, but Century Associates, as the copyright holder. All of the other films list Paramount Pictures. Any idea why this is, or what Century Associates is/was? A quick search of the US copyright database at copyright.gov reveals that that company held copyrights on several other films, such as Escape from Alcatraz and Players, but that still doesn't really shed light on who or what it was.
All the listed films were distributed by Paramount, so I'd guess Century Associates was some sort of production company associated with or branched off from Paramount, perhaps created as a financing partner like Skydance Productions was for Star Trek Into Darkness and Mission: Impossible -- Ghost Protocol. Or, well, no, if they were the actual copyright holder, that wouldn't be their role. Perhaps it served some legal purpose, then. Or maybe it was the corporate name associated with one of the Paramount executives at the time.
Maybe for tax reasons too, and so that the studio could say to performers with a percentage, "It's not showing a profit yet."
Probably some sort of shell corporation or the like, since, as Christopher notes, it was only involved with Paramount (and only existed for a short time, according to IMDB). Google turns up this court case in which they were involved. Interesting bit of trivia there -- ABC licensed Star Trek--The Motion Picture for $9.524 million (adjusted for inflation, $27,548,285.58).
Well, they certainly stalled on paying net royalties for years, so you may have a point. In the early 80s, there were investment possibilities for films that were crossed (the money you put into DOWN & OUT IN BEVERLY HILLS also goes into RETURN TO OZ, or rather, you don't get paid returns on HILLS until the losses on OZ get added up.) A friend of mine's dad had some kind of investment thing on those, I don't know if it was because of stock he owned or it was some other kind of offering, because the mid 70s tax shelters were already pretty much gone from films before that. Maybe there was something like that on TMP with STARTING OVER? Only other possibility I can think of is Century Associates was the bank that loaned the studio the money to make the film, but I can't see the copyright ownership going to them on that basis unless Paramount would default on paying them. Man, I just got a headache thinking about all this.