Dec 10 (Reuters) - A majority of U.S. central bankers believe they will need to cut short-term interest rates next year, but are widely split over how much, with a large group opposed to any cuts at all and three penciling in a rate hike.

And in a move unprecedented in the history of the Fed's so-called "dot plot," six policymakers indicated they didn't support even Wednesday's quarter-point rate cut, penciling in 3.9% as the appropriate year-end rate for 2025.

The target rate range after Wednesday's rate cut is now 3.50%-3.75%.

The median policymaker view for next year calls for one further quarter-of-a-percentage point cut - the same as the 25 basis point reduction they had expected three months ago. But only four policymakers actually wrote down a single rate cut next year, with another four expecting two cuts and four others penciling in even more.

   Seven of the Federal Reserve's 19 policymakers feel that borrowing costs should not fall at all next year, including the three who see rates as appropriately higher at year-end 2026 than now, according to projections released on Wednesday.

Forecasts for the policy rate at the end of next year ranged from 2.1% to 3.9%.

The median policymaker's estimate of a neutral level that neither brakes nor stimulates the economy remained at 3%.

The Fed's so-called "dot plot" of policy rate expectations does not say which policymaker made which forecast.

But it does shed some additional light on the depth of their internal divisions as they head into a new year, one that will bring not only the usual reshuffling of voting rights among Fed presidents but a new Fed chair to take over from Jerome Powell after his term ends in mid-May.

The Supreme Court in January will hear arguments on Trump's attempted but contested removal of Fed Governor Lisa Cook, which if successful could open a second seat for Trump to fill with a dependable proponent of easier monetary policy. 

President Donald Trump has said whoever he picks for the Fed chair job will support lowering interest rates further, but the number of Fed policymakers opposed to more rate cuts suggests that winning consensus on such a move will be difficult. 

Wednesday's decision drew three dissents. Kansas City Fed President Jeffrey Schmid and Chicago Fed President Austan Goolsbee had wanted no change to the Fed policy rate, while Fed Governor Stephen Miran for the third time had supported a bigger half-point interest-rate cut.

The median forecast is for a 4.4% unemployment rate by the end of next year, unchanged from what was reported for September, the most recent data available.

Inflation by the Fed's targeted metric - the 12-month change in the Personal Consumption Expenditures price index - is now expected to end this year at 2.9%, before dropping to 2.4% next year, versus the 2.6% projected in September.

Policymakers forecast core PCE inflation, which they use to gauge the persistence of inflation pressures, to end this year at 3.0% and 2.5% next year.

The Fed targets 2% inflation.