What is the mechanism by which the government expands the amount of money in circulation?

It is my opinion that the government cannot print money to pay debts, but when the treasury prints money to expand the amount in circulation how is the ownership controlled?

It is not at all clear what you are asking:

1. If you are asking about physical currency - printing currency does not create money. The Fed holds government notes to back all the money it has the Bureau of Engraving print and the individual banks buy the notes from the Fed on a dollar by dollar basis.

2. The Fed can increase the money supply in several ways:

http://en.wikipedia.org/wiki/Monetary_policy#Monetary_policy_tools

A. It can reduce interest rates so more people are want to borrow.

B. It can decrease the reserve requirements so that banks can lend more for each dollar they have.

http://baselinescenario.com/2008/11/23/federal-reserve-for-beginners/

Either way, the money is really created by the individual banks, not by the Fed. (Which is why the Fed can't do much about the current crisis: the banks don't want to lend)

C. The Fed can increase the money supply just by creating money,

http://en.wikipedia.org/wiki/Open_market_operations

but it generally does not want to do so.

http://www.npr.org/templates/story/story.php?storyId=99927343&ft=1&f=94427042

http://en.wikipedia.org/wiki/Monetary_policy