The Social Democrats (SPOe) of Chancellor Christian Kern, 51, are battling for second place against the far-right Freedom Party (FPOe) led by Heinz-Christian Strache, 48, for around 25 percent of the vote, followed by several smaller parties.
Black and blue
Most experts say that, if the results are as predicted, Kurz will likely form a coalition with the far-right, the first such tie-up of black and blue -- the parties' colours -- since 2007 and only the third since 1945.
When the FPOe entered government in 2000 under Joerg Haider -- who praised Adolf Hitler's "orderly" employment policies -- Austria was briefly ostracised. But Europe is now more used to nationalists and the party is seen as having mellowed.
Business as usual
The next most likely is (yet) another "grand coalition" of the OeVP and the SPOe. The two have ruled together for 44 of 72 years since 1945. No post-war Austrian government has been without one of them.
Whether they can stand to work together again after 10 acrimonious years is unclear. Kern may have to quit, as he has said the SPOe will go into opposition if it doesn't win the election.
Reds get the Blues
The SPOe have been in coalition with the FPOe before, between 1983 and 1987, but this was before the latter moved sharply to the right. An SPOe party motion in 1986 banned any future coalition with the FPOe.
But with some overlaps on social policy -- the minimum wage, pensions - the taboo could potentially be broken. The two parties have already been governing together in Burgenland state since 2015.
Generally however the SPOe and FPOe remain far apart on key issues and a tie-up could tear the Social Democrats apart.
One of the big parties could form a coalition with one or some of the smaller ones -- the Greens, the liberal NEOS or the Pilz List. But each has single-digit poll scores and might not make it into parliament.
Alternatively there could be a minority government, potentially sparking turmoil in a country that traditionally has been a byword for stability at the heart of Europe -- and even triggering another election.
President Alexander Van der Bellen has to approve the new government.
Whether he would give the green light to any involvement by the FPOe -- which is ambivalent about the EU -- is unclear.
Van der Bellen, who narrowly defeated the FPOe's Norbert Hofer in December to become head of state, has said any government has to ensure Austria is "at the heart of Europe". A refusal to approve the coalition could spark a constitutional crisis.