Recent searches have turned up two different estate notices that listed all of the next of kin of the deceased. One of the men I was searching for died in Jefferson County, New York in 1855 and the other in Niagara County, New York in 1864. Both of the notices were found in Albany, New York newspapers. I assume that because Albany is the State Capitol that Surrogates around the state were required to publish these legal notices there as well as locally. The page from 1855 is filled with tiny print and notices from around the state. There are fewer notices on the 1864 page, but again they seem to be state wide. I've also found that many papers around the state picked and repeated stories published in other papers so you may find something about your ancestor published in a paper far from where they lived.
I use Old Fulton Postcards to access old papers from around the state. To use the site effectively be sure to read the FAQ's. Also keep in mind that the site uses OCR technology for searches and while it works very well, some of the older papers were in rough shape when filmed and an OCR search may not work. If you don't find what you are looking for and you have a date you can try searching the old fashioned way, by browsing page by page.