My apologies, I think we're at cross-purposes here.

I do indeed have direct experience of dealing with death and probate here in Ireland.

The Obituary section of the Irish Times, a national newspaper, runs weekly. The national newspapers in the US have obituary sections too. These are what I mean by 'Obituaries'. These can be see online too.
In Dublin, for instance, a death notice only is the norm. The Irish Times for example, does not publish paid-for obituaries.

Practice outside the major cities, in the country areas, varies. I've known people who died in Sligo and Leitrim and Donegal and Cork and only had a death notice on radio.
In the local papers, paid-for notices with photographs and detail of the persons life are different and that's where my confusion lay.

As far as I know, there is no legal requirement to post any sort of notice of a death here in Ireland. As far as notification goes, your estate will not be wound up unless the probate office is notified with the will (or not), the appropriate forms and the death certificate.

Probate, whether with a will or not, is a long process here too.
Yes, in my experience the undertaker bills you after the funeral.
If there is any thing else, just ask.
Hope this helps,
E