Looking through the top sites that I have, I believe it looks for any of the following:

A <link rel="shortcut icon"> with some minimum resolution. A <link rel="apple-touch-icon"> with some minimum resolution. A regular favicon with some minimum resolution.

I'm not sure what the exact minimum resolution is, but 128x128px images appear to work fine, so I would try that.

Thanks, I'll try that!

But there is no official snippet on this ? Mozilla has all kinds of documentation pages, I can't believe there's no official word on which relationship value to use.

Oh, I just found this:

The media, type and sizes attributes allow the browser to select the most appropriate icon for its context. If several resources match, the browser will select the last one declared, in tree order. As these attributes are merely hints, and the resources may be inappropriate upon further inspection, the browser will then select another one, if appropriate.

Note: Apple's iOS does not use this link type, nor the sizes attribute, like others mobile browsers do, to select a webpage icon for Web Clip or a start-up placeholder. Instead it uses the non-standard apple-touch-icon and apple-touch-startup-image respectively.

The shortcut link type is often seen before icon, but this link type is non-conforming, ignored and web authors must not use it anymore.

From "icon" section of https://developer.mozilla.org/en-US/docs/Web/HTML/Link_types

That helps clarify a few things.