What would you call the stylistic omission of punctuation?

The best existing candidates have both been aired. As I said in my comments on Oerlekens, one problem is that ‘the Greeks did not have a word for it’. Indeed, they did not have punctuation at all. Failing the Greeks, the Americans are very good at coining words and phrases. So ‘run-on’ is in origin an American English expression.

But today’s Greeks do have a word for punctuation which might do: stixi (στίξη). It is derived from the ancient word stichos (στιχος), meaning a rank of soldiers. But the word came also to denote musical notation. From that it must have been adopted as the best word for punctuation.

From there, we might be able to construct the literary term Matthew Sbarr is seeking.

To turn it into its negative, you would add the *privative alpha, as in astixia. It might be astixis; or it might be astichism. Either would be a legitimate coinage. Because neither has been used before, so far as I can discover, you have a free choice. I prefer the former.

The trouble with this, however, is that before it can be used, you or someone has to publish an article on the subject and hope some readers run up the flag and salute!

Short of that you are left with ‘run-on’ and ‘stream of consciousness’, neither of which is ideal.

As a last resort, I wonder if ‘the Germans have a word for it’: they often do! In fact, looking up the word unpunctuatedness, I find the word unpunktiertheit.

This, in turn, has led me to discover that critical commentators on Joyce do use the term unpunctuatedness to express the quality of some of his writing. For example, Derek Atridge uses it in Joyce Effects. This refers to the quality of the practice rather than to the practice itself. But there it is.

The first thing that came to mind was James Joyce, and more specifically Ulysses, where he uses a narrative technique called stream of consciousness:

In literary criticism, stream of consciousness is a narrative mode or method that attempts to depict the multitudinous thoughts and feelings which pass through the mind.

As the Wikipedia-article mentions, he didn't invent it and wasn't the first to use it.

Note that not all punctuation is excluded, as can be seen in this sample that is also quoted on Wikipedia:

a quarter after what an unearthly hour I suppose theyre just getting up in China now combing out their pigtails for the day well soon have the nuns ringing the angelus theyve nobody coming in to spoil their sleep except an odd priest or two for his night office the alarmlock next door at cockshout clattering the brains out of itself let me see if I can doze off 1 2 3 4 5 what kind of flowers are those they invented like the stars the wallpaper in Lombard street was much nicer the apron he gave me was like that something only I only wore it twice better lower this lamp and try again so that I can get up early

Proper names are still capitalised, and the space is not omitted.