Homescreen icon requirement

in //src/chrome/android/java/res/values/dimens.xml and app_banner_data_fetcher.cc

 <dimen name="webapp_home_screen_icon_size">48dp</dimen>

Splash screen requirement

TLDR: There are 2 layouts for splash screens. You get the "small icon layout" if the icon you provide is <= 80dp. You get the "large icon layout" if it's over >80 dp. Ideal size for splash screen is 128dp. (There is also a way that a non-provided icon is used, though it's unclear what that is.)

// from chromium   /src/chrome/android/java/res/values/dimens.xml
<dimen name="webapp_splash_image_size_ideal">128dp</dimen>
<dimen name="webapp_splash_image_size_threshold">80dp</dimen>
<dimen name="webapp_splash_image_size_minimum">48dp</dimen>

There are three possible layouts for splash screens, which is chosen based on whether an
icon was auto-generated by Chrome and whether the icon is bigger than a threshold.

see how the splash layout and icon is chosen in //src/chrome/android/java/src/org/chromium/chrome/browser/webapps/WebappActivity.java

So far, our magic numbers are 48dp and 128dp...

dp and px

For phone-sized android devices, we mostly care about hdpi and up. (The Android One is hdpi) You can ignore anything less than hdpi

For example, the nexus 5 and nexus 6p are xxhdpi and xxxdpi respectively. (four-x doesn't exist yet, phew!)

So what do we need?

I dumped our key dp numbers into http://androidpixels.net/ (and hacked the page with devtools) for this 💰💰💰 screenshot:

So.. tl;dr:

If you'd like to provide native rendering of icon for home-screen and splash-screen across supported screen densities, you should provide an icon in these sizes:

72, 96, 144, 192, 256, 384, 512

And all of these should be explicitly indicated in your manifest.

Update: conversation below indicates you need fewer than this:

192, 512

Dec 2020 edit: some related stuff in #11762