(REUTERS) - The Eurozone banking system starts the new year awash with record levels of liquidity but few signs that institutions are prepared to lend to each other, leaving money markets frozen.

Most of the near half trillion euros of three-year funds borrowed from the European Central Bank in the last week of 2011 have made their way back to the ECB's overnight deposit account.

Use of the facility was close to 450 billion euros on Monday night. But, reflecting the dislocation in short-term funding markets, at least one other bank borrowed 14.8 billion euros from the ECB's punitively priced emergency lending facility.

What happens to the excess liquidity in coming weeks will be key. But with banks facing heavy refinancing schedules this year, those looking for a revival in money markets may be disappointed.

My sense is that we will see some easing of tensions, but that's a natural seasonal thing, said Simon Smith, chief economist at FxPro.

But it's unlikely to be that substantial because of the bank refunding that needs to be done and the three-year money was in part intended to help with that.

Benchmark three-month euro Libor rates fixed a basis point lower at 1.26857 percent, and down around 6 basis points since the injection of three-year funding.

But the spread over equivalent maturity overnight indexed swap (OIS) rates has barely budged - it stands just a couple of basis points lower at 88 basis points - and RBS said there is unlikely to be a material tightening.

The reduction of tail risk for banks, where the ECB has effectively backstopped the system reduces counterparty risk to the extent a Lehman type event is a lower probability, strategist Harvinder Sian said.

Until the sovereign risk is reduced (spreads) are unlikely to trend narrow - and our view remains much more cautious in that sovereign defaults are likely in 2012, starting with Greece.

Concern over banks' exposure to the sovereign debt crisis has closed money markets and longer-term financing markets.

Societe Generale calculates that the roughly 200 billion euros in extra funding available to banks since the three-year tender only corresponds to an estimated financing gap for 2012 based on longer-term debt redemptions and deleveraging.

Even with another three-year tender in February, that means banks are unlikely to use the cash to buy Eurozone government bonds, the so-called carry trade, anticipation of which drove shorter-term Italian and Spanish bond yields sharply lower at the end of the year.

Banks are torn between using cheap borrowing to boost profits and intense market and regulatory pressure towards deleveraging, SG analysts said.

We continue to believe that the latter is too strong a force. The large (three-year cash) take-up should reduce the speed of asset selling, but we doubt it will lead to aggressive buying of sovereign bonds.

Banks did, however, cut their take-up of one-week ECB funding by just under 15 billion euros on Tuesday , although it is quite usual to see a reduction in such borrowing as the monthly maintenance period advances.