Homesteading claims were assessed by the General Land Office GLO which later became the Bureau of Land Management BLM. The GLO had offices in every district in which lands were sold. Records were generally not sent to Washington. Records would be kept at the local GLO office or sent to a local courthouse.
Lands were surveyed prior to being opened for sale or homesteading. Most Parcels were in some form of a square or rectangle as this was the easiest shape to use when surveying and dividing the land. The GLO would then draw a map or several maps of the area to be distributed. Individual parcels would be marked on the map with a number. Each number would reference a written set of coordinates designating it's boundaries.
The land would then be distributed either through a land rush (first to claim the property and return with the appropriate flag which would be numbered) or through a lottery system (as your name was drawn you could select the parcel you wanted) or through a simple process of waiting in line.
To stake a claim you had to prove you were the head of a household or over the age of 21 or had served in the U.S. military or Navy and had never taken up arms against the U.S. You would then pay a small fee and would be given a certificate indicating you were homesteading the property.
After 5 years you would return to the GLO and request to be given a patent for the homestead. A GLO agent or surveyor would visit your property and observe that you had made improvements to the property equal to $1.25/acre. You would then receive a patent/deed/title for the property and would file it in accordance with local and state laws.
Local GLO offices would report back to Washington the number and type of Parcels assigned as well as the revenue generated. Washington Bureaucracy has been in place longer than most people realize. The homesteading of Western lands was just another in a long series of land distributions by the GLO. From the sale of lands in Ohio and Pennsylvania (back then called the northwest) to the distribution of lands in Florida, Alabama, Mississippi Distribution Of lands in Kansas Nebraska Texas. If it wasn't in the original 13 colonies The land was sold or distributed by the GLO. During these distributions a local GLO office would handle all the transactions before turning the land over to local and state control. These offices reported back to Washington little more than the land amount, the land type and the revenue generated.