Mr Key has timed his departure for Europe next week to ensure he will get to face the new leader's first question time in Parliament.
The results will be announced on Sunday a few hours after voting closes.
The House is in recess this week and resumes on September 17, the day Mr Key leaves.
He said at his post-Cabinet press conference yesterday that he made sure he wouldn't be leaving until after the new leader's first day in the House. Asked who he believed would win, he said Mr Cunliffe.
Tonight's candidates meeting in Christchurch is the last for the three MPs contesting the vacancy, Mr Cunliffe, Grant Robertson and Shane Jones.
A 3 News poll last night suggested that the fact Mr Robertson is gay affects people's perceptions of his chances of winning an election.
When asked whether public opinion about his homosexuality affected his chances of becoming Prime Minister, 58.5 per cent said yes and 41.5 per cent said no.
Among Labour supporters in the poll, 48.3 per cent thought it would affect his chances.
Mr Robertson said the poll asked voters to read the minds of other New Zealanders and say what they think other people think.
"What I experience from people themselves is that they don't view this as an issue.
"Yes, there will be some people in our community for whom this is an issue and I say to them, 'Judge me on the policies I am putting forward
and on the values of the Labour Party which I believe are the right ones for New Zealand'."
Mr Cunliffe has been ahead in all of the public opinion polls, with Mr Jones second and Mr Robertson, the present deputy leader, third.
Four of the six smaller affiliated unions have recommended Mr Cunliffe, but none is insisting its delegates vote for him.
The two biggest unions, the Engineering, Printing and Manufacturing Union and the Service and Food Workers Union - whose combined votes will make up just over 11 per cent of the total - are leaving it up to members and delegates to vote.
Mr Robertson said more service workers turned up at the Wellington meeting than any other. He was confident of their support and of good support from the EPMU as well.
Outgoing Labour leader David Shearer announced his resignation on August 22 after his core caucus backers withdrew their support.
Labour Party election
Voting closes for the new Labour leader midday Sunday.
The results will be announced a few hours afterwards.
Prime Minister John Key has delayed his departure to Europe to face the new leader's first question time in Parliament.
- Audrey Young of the NZ Herald
