How did provinces or states form out of a early cities and territories in North America when it was settled by Europeans?

by Sparkiran

How did the state lines get drawn and why is Missouri its own entity and Arkansas its own separate one? Is it due to population density? Company interests? Political or warfare disputes?

MrDowntown

There are complex stories for each of the US states (except maybe Hawai’i) involving the original colony grants, overlapping claims, huge misunderstandings of geography, cession of unsettled territory to the new nation, and the later formation of territories and new states in vastly different geographic regions. In very general terms, the original colonies were given royal grants to specific territories. After the United States was formed, some of those grants of western lands became the Northwest Territory, from which new states were anticipated to be formed. Soon followed the Louisiana Purchase and other lands from which new states could be organized and admitted to the Union. The general intention was that new states would be roughly the same size, though that size grew as the arid West was considered, and Texas and California had their own stories.

The details are given in Boundaries of the United States and the several states, a US Geological Survey book available as a PDF here or older versions on archive.org or Google Books. Mark Stein's book How the States Got Their Shapes is a popular book telling the same tales.