I know, I just wrote a post with almost this same name. But since I wrote that last post, I realized that I hadn't really explained most of what I was talking about. So here is the real story.
Genealogists need to know quite a bit about probate procedures, both current and historical. Maybe not as much as a probate attorney, but enough to puzzle out what happened in the probate estate and who got what. Surprisingly, the language of probate law has changed very little for hundreds of years. Wills written in the 1600s and later sound just about like a formal will does today and they essentially accomplish the same thing; transfer of both titled and personal property to heirs and devisees upon the death of the testator. OK, so now the legal jargon begins. It might be a good idea to get the basic vocabulary down. Here is a link to a PDF file called Estate Planning Basics: A Vocabulary from Utah State University Extension. This should give you a pretty good start.
Now, let me be as clear as possible about what might happen to your piles and mounds of genealogical research if you were to die. There are really only about three possibilities:
A. All the papers and other documents are immediately dumped in the trash. The computer disks are wiped clean and the computers sold or given away. (Also known as the worst case scenario).
B. The papers etc. are kept for an indefinite period of time and then thrown away.
C. Some kind and interested soul retrieves the piles and the computer files and tries to make some sense out what you did and were trying to do.
You might notice that I didn't say anything about probate. The reason is not simple to explain, but I will try.
There are two basic kinds of property in the world; titled property and untitled which is usually personal property. Real property falls in the category of titled property. Unless there is some formal method of ownership for the property, such as the title to a car or a stock certificate, everything in the estate is usually lumped into the category of "personal effects, clothing etc." Any titled property has to be transferred to the heirs by the personal representative (aka administrator, executor etc.) of the estate. There are, by the way, feminine versions of the words, see administratrix and executrix. Anyway, here things start getting complicated. Between the time a person dies and the time at which a personal representative (the common term today) is appointed to administer the estate, technically no one owns anything in the estate. Notwithstanding this legal issue, it is common for the survivors of the deceased to dispose of "personal property" deemed without value long before the matter ends up in court in a probate. See A, B, and C above.
If you die and have no property to speak of and no will (intestate) then no one really cares and whatever you possess at the time of your death is usually thrown away or divided up by anybody who happens to have an interest in you (your descendants or other relatives). There go the genealogy documents as outlined above.
Now what kind of property are computer files and piles of research and documents? They are personal property. Since they have no ascertainable monetary value, they are of no interest to the estate. So, unless someone claims them, they will get disposed of as (again) outlined above.
But what if you leave a will and give the stuff to some relative or descendant (child, grandchild etc.)? The answer here is so what? Unless the person to whom the stuff is given really wants it and knows what to do with the stuff, then see the above possibilities again again. This is called a specific devise or bequest. The key here is that the person who gets the stuff doesn't have any obligation to keep it. They can sell, transfer or throw it away if they want to.
In old wills it is not uncommon to see things like a spoon or tool given as part of the will. These specific bequests were and are enforceable at law, but again, so what? If the person who gets the spoon decides to throw it in the trash, it is theirs to do so. The same with genealogy stuff.
OK, so now you might get the picture. Estates deal primarily with property owned (titled in the name of) the decedent at the time of death and incidentally with personal effects. But only when those items have some intrinsic value, i.e. paintings, collections, antiques etc., is there any real issue in their disposition.
Now it is the nature of heirs to fight over things that have "sentimental value." I have commonly seen fights over who gets the photo albums and things like that. But I don't recall ever hearing about a discussion of a fight over who got the piles of genealogical documents. Commonly, they are stored in basements and garages until they are thrown away. One of my cousins died and left a stack of boxes of genealogy. I have been talking to the family now for over a year about looking to see if there is anything of value and have yet gotten anyone to show me the boxes, which I assume are stacked in someone's garage.
So, the key here is to identify exactly who and under what circumstances will "inherit" the genealogical documents upon your death and this should be determined long before death so that the person who receives the documents etc. will know what has and has not been done. But, I would say, good luck finding someone in that category. Meaning it may be impossible.
That is why I come to my conclusion to put everything of value online and hope the place you put it survives.