There are very good reasons for the map. Under the Common Law, which our country was formed from, title to land always flows from the sovereign. First, it was from the Crown, then, later, our federal government, as the successor sovereign to the Crown. All attorneys are taught this in law school. It is woven through our constitution, its amendments and all court decisions interpreting it. In the east, it didn't take that much land to support a family, so the land grants were smaller. When I first started practicing law, standard practice was to trace title all the way back to the land grant. Now, titles are not checked back nearly so far. Land grants which were given by the English crown were honored, if the present holder foreswore the British Crown and declared loyalty to the US.
By the time of the Civil War, the land east of the Mississippi had almost all been granted out, except for a few pockets no one wanted at the moment. That's the reason for the eastern part of the map. in 1862, the first Homestead Act was passed, 160 acres each to "genuine homesteaders." The idea was you had to live on the land and there were other requirements. The political motive was to promote the ownership of land by former slaves, women, young men - any one who hadn't taken up arms against the Union. Of course, there was a lot of corruption in the system, with large land owners splicing together tracts occupied by servants and even worse abuses.
Problem was, as you went further west, the more land it took to support a family. Also, the original idea of the 160 acres and a family farm was unworkable in the west. It wasn't crop land and it took a helluva lot of it even to run enough cattle to get by, which is still the situation in Nevada. In fact, the last Homestead Act, sometime around 1915-18, allowed 640 acre grants in western Nebraska (still not enough for grazing). So the Crown (Federal Government) was left holding vast tracts of land not wanted by anyone. This is the case till today.
Over the years, a patchwork system of leases, mineral claims, grazing leases, etc., developed. The BLM was created to try and bring some semblance of order to the situation. I'd say their results were mixed, but it was probably better for the consolidation.
Now, for an important part of the Common Law, which we've lived under for centuries. One cannot adversely possess (squat) against the Crown. IOW, your family may have occupied land in federal ownership for generations. Legally, it means nothing, since all title comes from the federal government - nowhere else, period. That's the reason these fanciful notions of Bundy that the state of Nevada owns the land in question amuses me. Nevada doesn't support it at all. (Incidentally, if Nevada had not come out with a strong constitution repudiating armed rebellion, it would not have had a ghost's chance of being admitted to the Union.) His position, and similar ones, flies in the face of centuries-old accepted law, which is part of the foundation and constitution of our country was built. Our founding fathers would just shake their heads at the thought that a state could hold title superior to the title of the federal government. That was settled first in 1781 and given a big final "exclamation point" in the Civil War. My GGF, a member of the Union League, had all of his property confiscated by the confederate state of Alabama in the 1860s. He sued for compensation immediately after the war. He had no luck. They defended successfully on the grounds that the property was taken by an illegal rebel government (although the faces in government in 1867 were almost the same). So much for state ownership of federal lands...
