Alan:
The split between the relatives is according to a set formula, based on their intestate share in the estate. The rules in Illinois are most likely fairly similar to those in my jurisdiction, but I'm not going into that particular rabbit hole, because they probably involve
per stirpes division, with the relative shares based in how many inhabitants of each
stirp survived Ms. Maier (have fun with the Law French/Latin roots of
per stirpes division

). Just understand that some people get more than others, because they are either more closely related to the deceased, or because their portion is a part of a larger share that is shared equally between several others - often siblings.
It is the privacy interests that are protected by the rules - there is no particular public interest in knowing how many second cousins of the deceased end up being entitled to a share, or who they are. The Court isn't there to make public the details of someone's extended family tree.
The beneficiaries themselves share the benefit of those assets according to that formula, but they don't end up owning the assets themselves - the administrator owns them and holds them in trust. The administrator might own them for a long time or might sell them promptly. The terms of the order appointing the administrator may include a requirement that the estate be held open for a certain minimum time. For as long as the assets are held by the administrator, they will most likely generate revenues to the estate, and those revenues are what the beneficiaries share in.
Registration or non-registration is essentially irrelevant to the Vivian Maier beneficiaries, because although registration will help protect against future infringement, and will no doubt have been undertaken by the administrator, the future stream of income or proceeds from the sale by the administrator of the copyright interests won't be registration related. Registration is mostly there to help you go after people who try to appropriate the benefit of copyright from you.
In the Vivian Maier case, the Court has already granted really important and valuable remedies that are worth a lot more than the statutory remedies. The facts of the case made it necessary to spend the time and money to seek those remedies.
For most of us, we would prefer to be in a position to choose to pursue the relatively quick and inexpensive and reasonably generous statutory remedies, or to pursue the potentially slow and expensive but much more extensive remedies that are outside of the statutory remedies. It turns, as do many things, on how much is involved. But if you haven't registered, you don't have the choice.