I am interested in a system where the state prints new money to cover
all its expenses. (There is no direct tax collection.)
I'm interested in anything you might have to say about this system,
but to keep things concrete:
(1) Has it been tried?
If one wants to take a very strict definition of "tax", it may be possible that some resource-producing countries have no "tax." Instead, they have revenue from commodity exports. However, such cases are somewhat of a stretch.
(2) Have economists studied this system? Are there any consensus
Modern Monetary Theory (MMT) is one school of thought (part of post-Keynesian economics) that examines the details of government funding. The argument is that all government spending is effectively "paid for" by issuing money.
However, MMT theory also argues that "taxes drive money." In order for government-issued money to have non-zero value in exchange, it is necessary to have taxes, which can only be paid using the government-issued currency. If taxes were abolished, the currency would have zero value (or the prices of goods expressed in the currency unit "go to infinity," which is effectively a hyper-inflation.
MMT is popular on the internet; you can easily find a lot of information via a search engine. One academic site is fairly central: http://neweconomicperspectives.org/
Of course, not everyone agrees with MMT. But the online debates would cover the issues that this question discusses.
As for a consensus view, the argument that taxes are needed for the currency to have value is probably close to consensus, although the wording would be different. The Fiscal Theory of the Price Level is a theory that the expectations of future taxation (primary surpluses) is what drives the value of the currency. If only money were issued, interest rates would have to be 0% forever, and that allegedly gives rise to unstable equilibrium (with prices expected to shoot off to infinity). There is lot of related discussion with regards to the "governmental budget constraint" and "Ricardian/non-Ricardian" policies.
Schools of thought that rely on the quantity theory of money would view the rapid creation of money as being a direct cause of hyperinflation.
(3) Does it have a googlable name?
As I noted above, searching for:
- Modern Monetary Theory (or Chartalism);
- the Fiscal Theory of the Price Level;
- the Governmental Budget Constraint;
- Ricardian/non-Ricardian policies;
should give a lot of material to read.