Brian Cowen is well ahead in the public mind as the most likely successor to Bertie Ahern as leader of Fianna Fáil, but there is no clarity about who his main rival, if any, will be when the Taoiseach steps down.
The biggest surprise in the poll is the emergence of the Minster for Justice, Brian Lenihan, in joint second place with Micheál Martin, just six months after he joined the Cabinet.
The Minister for Education, Mary Hanafin, comes in fourth and the Minister for Foreign Affairs, Dermot Ahern, fifth in the poll.
Of course the decision will be made by the Fianna Fáil TDs and not by the public, but they will be keenly aware of how the voters might react to any new leader.
A striking feature of the poll is that Brian Cowen has a much bigger lead among Fianna Fáil supporters than he does among the wider public. Among all voters he attracts the support of 28 per cent, but among Fianna Fáil supporters that jumps to 46 per cent.
Surprisingly, there is hardly any variation across the country in the level of support for the Offaly man. He attracts 29 per cent support in Dublin, precisely the same figure as the rest of Leinster. His support is marginally lower in Munster and a bit lower again in Connacht-Ulster.
In terms of age groups Mr Cowen also has a good spread, although he is significantly stronger among the over-50s than those in younger age brackets.
There are two significant variations in his level of support. Mr Cowen is much stronger with middle-class voters and farmers than he is with working-class voters. In gender terms he is much stronger among men, with 33 per cent support, than with women, where he gets 23 per cent.
The two Ministers who tie in joint second are well behind, with 10 per cent each. Mr Lenihan and Mr Martin are level among Fianna Fáil voters but the Minister for Justice is strongest among Labour and PD voters, while Mr Martin is ahead among Fine Gael and Green supporters.
Mr Lenihan's highest ratings come from the over-65s and working-class voters, while he is stronger among women than men. His support is spread evenly across the regions of the country.
By contrast, Mr Martin is very strong in Munster and weakest in Dublin and Connacht-Ulster. In class terms he is also strongest among the lower-income groups.
Mary Hanafin scores best in Dublin, where she is running in second place to Mr Cowen, and she is also significantly stronger among women than men, with almost twice as much support. In age terms the 18-25 group are her strongest backers.
There is very little variation in support for Dermot Ahern across the country or among different age groups or social classes. The only surprise is that he is stronger among Fine Gael and Sinn Féin voters than he is among Fianna Fáil supporters.