How is a new department born? I can think of two possible ways in which a new department is born: one, the university decides to start teaching a certain subject, and in the other, an existing department splits into two (e.g. department of physics and astronomy -> department of physics + department of astronomy). If the answer in these two are different, please say so and I will split this question into two.


Clearly the initiative must come from a senior university administrator. Who though - the chancellor? The vice chancellor? The dean of the faculty?
Starting a new department is presumably very expensive. Where does the university find the money? Do new departments usually only start when there is a sudden source of funding (e.g. ___ big new discovery leading to a massive surge in student interest + external funding in the field)? Or do universities spend years saving money before starting a department?
Once the decision is made to go ahead, how does the university go about it? Do they hire a new professor who works in the field, provide her with a budget, and let her hire everyone else? Or do they decide on every individual hire by committee, which is not always made up of people expert in the field or affiliated withe the university?
In all of the cases I have heard of, existing departments split. Sometimes not one, but sometimes faculty from several existing departments split to form a new one. For example, faculty from mechanical engineering, physics, chemistry, and maybe math may form a new department of materials sciences.  Or faculty from math, statistics, computer science, biology, and a variety of engineering departments may form a department of computational science. Oftentimes, such departments are born after there is already a graduate or undergraduate degree that exists in this area and to which the involved faculty members have previously contributed.

In the cases I know of, the initiative has always come from the bottom, not the top. Typically, this has to do with faculty members feeling that there is a critical mass of faculty in a variety of departments to create a new degree program, and they later realize that they may as well build a department around it. The other reason is that the members of such a group may feel that the department they are in does not value their work -- this is, for example, how many statistics and applied math departments started as forks of mathematics departments dominated by pure math faculty who did not appreciate the work or style of the stat or applied math researchers.

In all of these cases, new departments consist of existing faculty. So at least as far as faculty salaries are concerned, this is often not substantially more expensive than the existing structure. Where things get more expensive is that departments typically duplicate support structures as well, such as staff, web site maintenance, etc. But it is not necessarily true that this is "very expensive" as you state.