Printer Resolution and Stuff

That sounds nice in theory, but most people do not get the concepts of sampling and resampling much at all, and are incapable of recognizing when resampling methods matter. For a lot of people, it won't make much difference in a majority of photos, so they are inclined to ignore the topic completely, but they may get burned when there is some fine periodic detail and it blows up on nearest neighbor. Sending an image to the printer at a PPI that doesn't cause resampling in the printer driver allows one to see a magnified view of the pixels that the printer is going to (try to) print. It isn't exactly the same, because ink bleeds randomly and there is usually dithering, but there is a pixel-to-pixel correspondence.

For a good quality interpolation and sharpening one can try (14 days free trial) Qimage www.ddisoftware.com/qimage-u/index.html

I'm a fan of almost everything about QImage but the GUI.

Oh well... Took me some time a decade+ ago :) Same as with Vuescan.

I don't know Qimage. I used sometimes Mirage which was quite good (but the GUI! ).

"Reasonably close" is a horrible target for nearest neighbor. If the printer prints simulated pixels (with smaller, dithered dots) at 360 PPI, then only 360 PPI, 180 PPI, 120 PPI, 90 PPI, etc, will print like the image looked on the monitor at 100%, 200%, or 300%, etcetera. All source pixels will render with 1:1 horizontal:vertical spacing, and evenly.

If you do a ratio like feeding a 360 PPI printer a 240 PPI instruction, then every other column and row of original pixels will be doubled in thickness, which can become obvious with a magnifying glass or if the subject matter is fine repeating details, but may be subliminal in normal viewing of most subject matter due to visual extinction. What if you're giving the print driver a 330 PPI directive, though? Now, every 11th column and row of original pixels is doubled, and this pattern is much lower in frequency and will not escape visibility through extinction, and it may be visible at normal viewing distances, even in non-repeating material.

Epson says print resolution of P900 is 5760 x 1440 dpi Maximum.

I used 2880 x 1440 dpi Epsons. I tried to feed them with 180ppi, 360ppi and sometimes even 720ppi files.

If you send the driver a 720 ppi file, be sure to check Enhanced Detail.

Yes I did. Today I don't have a printer.

That makes sense to have more resolution for the dither horizontally, since the spatial control is probably tighter horizontally than relying on the paper to advance with great precision.

What happens with 720? Does it drop pixels (NN), or does it reduce the size of the dither pattern for 720 PPI output?

ppi is RGB, dpi is about whatever ink is in the printer and nozzle configuration.

Why should it drop pixels?
I always set resolution in Epson driver at 2880 (best) which is really 2880 dpi only in one direction.

BTW. 720 x 2 = 1440, 720 x 4 = 2880

I'm not sure why you wrote that. By "output", I mean simulated pixels. The ink and dots are simulating pixels. 360 simulated PPI vs 720 simulated PPI.

I'm not very good in printing technology. I think Epson sprayed 2x4 dithered dots from every pixel of my 720ppi picture.
How it used nozzles goes over my head.

If you check Enhanced Detail and send the file at 720 ppi, the error diffusion halftoner uses the 720 ppi file in its entirety.

If the print driver is simulating 360 PPI output with its dithering, and you give it a 720 PPI instruction, it has to reduce the number of simulated pixels. If nearest neighbor is used, then it must drop every other column and row of pixels.

My query is whether this is what is done, or a better downsample is used, or the driver switches to an actual 720 PPI simulation (either automatically, or on command).

The latter, if you check Enhanced Detail and send the file at 720 ppi, the error diffusion plus blue noise halftoner uses the 720 ppi file in its entirety

That's good. If it can do that, what is the drawback of always using it, other than computation speed? Sure, each simulated output pixel will have less tonal precision, but the error should mostly disappear in aggregate, just like higher pixel-level noise disappears in aggregate with higher pixel density.