I published (posted if one prefers) two papers on SSRN based on my independent investigations into what I call "sources and sinks" of money.

Sources and Sinks of M1 Money in a Four Sector Model of the U.S. Financial System:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2257270

Financial Instrument Generation in the U.S. Financial System:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2458563

Every economic unit in the national economy can be classified using four sectors shown below:

> Fed | Banks | ---> Generators of Money \
Gov | Other | ---> Users of Money

In this model Gov means the Treasury branch of the federal government. Fed means the central bank also known at the monetary authority. State and local governments and all other non-bank units go into the Other sector.

A simplified model for the Bank sector balance sheet:

$ RB + RC + BC = TA + L* + EQ $

where RB means reserve balances held by banks on account at the Fed; RC means vault cash that banks purchase from Fed using reserve balances and hold to service the withdrawal of funds converted to currency in circulation; BC is bank assets also known as bank credit; TA means transaction accounts in the M1 money supply; L* means bank liabilities excluding TA; and EQ means equity.

Define M1 money supply as transaction accounts TA plus currency in circulation CC:

$ M1 = TA + CC$

The way currency in circulation CC increases is units in the Other sector make withdrawals of currency from the Bank sector. The increase of CC accompanies a decrease of vault cash RC and transaction accounts TA (assuming checking withdrawals only for simplicity):

$-{\Delta}RC = -{\Delta}TA = {\Delta}CC$

The Fed records the accumulated currency in circulation CC as a liability on its balance sheet. Prior to 2007, when there were no significant excess reserve balances in the aggregate Bank sector, the Fed would purchase Gov securities in the open market and hold those securities roughly equal to its liabilities CC. If the Fed purchases these securities from Other sector, and if Bank sector clears the payments between Fed and Other, then the aggregate bank records an increase of reserve balances RB and transaction accounts TA when Fed services the currency drain (the increase of currency in circulation):

${\Delta}RB = {\Delta}TA (when Fed buys securities from Other sector)

Since banks sell RB to Fed to purchase RC in the first place the Fed is replacing reserve balances that would have been drained by the withdrawal of currency in the absence of the Fed servicing the currency drain. Fed must do this to support the payment system, support the circulation of currency in M1, and maintain control over the rate of interbank lending and borrowing of reserve balances in the federal funds market.

When a bank makes a loan to Other, or when a bank buys financial securities (bills, notes, bonds) that were issued by Other or Gov, then this increases the M1 money supply as net new transaction accounts and increases Bank Credit in aggregate bank assets:

${\Delta}TA = {\Delta}BC$

Transaction accounts TA are bank liabilities. Banks develop Other Liabilities L* (M2 saving and time deposits; M3, M4, etc.) to keep reserve payments flowing in the interbank payment system even as the bank sector expands its balance sheet on both asset and liability side. The source of the Other Liabilities L* is the net reduction of TA:

$-{\Delta}TA = {\Delta}L*$

The delta notation means the net change in levels on the balance sheet of the aggregate bank sector over the accounting period used to keep the financial statistics. 

When the economy expanded prior to the financial crisis of 2007 the pool of reserve balances RB, provided by the Fed to the Bank sector, did not grow in proportion to the huge rise in Bank Credit BC, so the ratio RB/BC became progressively smaller and smaller. Economist Hyman Minsky explains this in his book Stabilizing an Unstable Economy: the bank sector can economize on reserve balances RB by rolling over and expanding Other Liabilities L* and issuing sufficient equity claims EQ. 

The bank sector creates the transaction accounts TA that convert to Other Liabilities L* and equity EQ. The Fed (central bank) must provide enough reserves to help the banks keep payments flowing, without being forced to sell some assets to Other sector, in order to hit their monetary policy goal of say 2% inflation. When money and credit markets are efficient and expanding credit Fed does not have to supply much reserve balances RB because banks try not to hold these non-performing assets. During the global financial crisis the Fed was forced to inject excess reserves and net transaction accounts into the Bank sector via Large Scale Asset Purchases (LSAP) because credit and money markets were frozen with distrust and this deprived the Bank sector of the ability to rollover and expand the sum of TA + L* + EQ necessary to hold the sum of RB + BC on the asset side of the balance sheet(s).

When Gov deficit spends it issues Treasury securities that are held as financial assets of Banks (in Bank Credit), of Other, or of Fed. Before 2007 when Other sector would withdraw currency from Banks then Fed would purchase Gov securities equal to the currency in circulation CC. Fed had to do this to control interest rates via jawboning, and when necessary, the ability to tune the level of reserve balances RB. When Fed buys securities from Other sector this injects reserve balances and transaction accounts into the aggregate Bank sector. The purchase or sale of securities by Fed is called Open Market Operations.

When Other or Gov transact among each other no bank liabilities are created or destroyed. The ownership of the bank liabilities either transfers to another unit in the economy during a purchase and sale of goods or via a credit/debt transaction. As long as credit/debt transactions do not involve Fed or Banks then no money is created or destroyed by the economic activities.