When to split/merge papers?

According to Gian-Carlo Rota, one of the secrets of mathematical success is to publish the same result many times.

I've split a paper once. I wasn't inclined to do it, but the paper was becoming huge so I was a bit worried -- 60+ pages, few people read papers that long. The other criterion was there was a natural way to split the paper into two useful papers. One turned out to be a "largely survey" 40+ page paper. Sometimes it's tricky getting papers published when they have a lot of survey material, which concerned me at the time. This allowed for the main result to be a short 20+ page paper.

In general it comes down to a cost-benefit analysis. Size of the paper is a consideration. How interesting the results are, that matters. Some people go overboard on fragmentation of their papers. For example, if you're publishing more than 4 papers per year all on essentially the same topic, it leads to confusion among readers as to where your results appear, and which papers depend on which.

My view is that you should always try to write short papers only; a long paper should arise only despite your best efforts to avoid it. In particular, each paper should present only one new idea or theorem (the proof of course might require more than one idea). This benefits both you and your audience. Your audience gains, because it will be easier to both find the right paper to read and read the paper itself. You gain, because you have a longer publication list.

And Rota's advice is quite right. Even one idea or theorem often deserves more than one paper, because there are different angles to present.