If you are going to leave it to your heirs or to chance, compile some information on collectors or dealers who would be interested in taking some or all of your collection. Let your family know which records you have that are particularly valuable and how much they might expect to get for then or your entire collection. Keep in mind that selling a collection, particularly if you want to get full value for the collection, is a great deal of work, unless you get an institution, collector or dealer who is willing to take it all. Also keep in mind that dealers need to make a fair profit on what they buy and would prefer not to obtain slow moving inventory. Selling may involve creating a list, circulating it to a focused audience, organizing the sale and packing and shipping the records. It takes a lot of time and there aren't many people willing to undertake such task.
The easiest way to dispose of a collection is all-at-once. That is, if you can find a buyer or institution that will take the whole thing, it is easiest on you. Unfortunately, price suffers. Piecemeal is the other option, but it takes much longer and doesn't guarantee that you'll be rid of every record anytime soon. If you have a large, high-quality collection, you might want to contact Kurt Nauck. He is very respectable and will handle everything to everyone's satisfaction. Dealers who sell 78s need to buy them, so contacting other dealers could work out. I list quite a few on my "Where To Get" page. If you want to sell it yourself and you have a lot of high-quality stuff (>$5 per record), you could post them on Facebook's 78 RPM Sell & Trade group or list on Discogs.com or even Facebook Marketplace or Craigslist.org. Sometimes even lesser-quality records can be listed. Finding a local buyer will save you packing and shipping.
Donating is also an option. Universities, libraries, archives and private public collections are all alternatives. If you think you want to donate to an institution, check it out and find one that is willing to take your collection now or at some time in the future. A collection doesn't need to be donated intact to just one institution but can be split among steveral. Some libraries that accept collections include:
When making a donation of materials to an institution, you might consider donating the funds to have your collection cataloged, hire staff, etc. Sometimes, even a small monetary donation along with a collection can do a lot to defray the costs of the institution acquiring it. Just the cost of shipping the records can get lofty.
Institutions may or may not be the best place for your collection, depending on what you want done with it. If you are looking for long-term, stable conditions from which future generations might benefit, libraries and archives are uniquely suited to that. A number of collectors feel that giving it to an archive and putting it in the garbage are nearly equivalent in terms of the number of people who ever hear the records again. Again, interview the potention recipient.
There is no perfect or easy way to find a home for record collections, unfortunately. For more information, consult articles in the ARSC Journal 1995 Vol. 26 No. 1 pp 53-61, the Antique Phonograph News January-February 1996, or the IAJRC's 86 page monograph entitled, "Assessing, insuring and disposing of jazz record collections."