By Martin Asser
BBC News website
Kadima was founded on the premise that Israel's long-term survival depends on safeguarding its Jewish majority and preventing Palestinian Arabs becoming the majority at any time in the future.
Kadima's plan was devised by Sharon but Olmert must carry it out
Demography was the motivation for Prime Minister Ariel Sharon's withdrawal of troops and settlers from the Gaza Strip last year and Kadima's election pledge to make future "territorial compromises" in the West Bank.
The idea is rejected by the former ruling party, Likud, which Mr Sharon was forced to split from to set up Kadima in November 2005.
But when Mr Sharon was incapacitated by a stroke in January he had not fully spelled out Kadima's intentions, so this job has fallen to his close advisers and his deputy, Ehud Olmert.
"In the coming period we will move to set the final borders of the state of Israel, a Jewish state with a Jewish majority," Mr Olmert told Kadima supporters in a televised speech on election night.
He added: "We will try to achieve this in an agreement with the Palestinians... If not, Israel will take control of its own fate, and in consensus among our people and with the agreement of our friends in the world, especially US President George Bush, we will act."
"The time has come to act," he reiterated. Indeed, the time probably has come already.
There is little expectation of any progress towards a negotiated two-state solution - especially since Palestinians voted for a Hamas government in January, and the militant organisation does not even acknowledge Israel's right to exist.
Mr Olmert has spoken of establishing Israel's final borders by 2010.
To do that, he wants to pull out of most of the land captured and occupied by Israel during the 1967 war, but to incorporate areas with large Jewish settlements into the future Israel.
Part of this land has already been annexed by Israel - East Jerusalem and the Golan Heights - although this move contravenes international law and has not been recognised internationally.
But the focus in the next few years will be on the large settlement blocs in the West Bank, such as Gush Etzion in the south, Ariel and Kedumim in the north, and Maale Adumim east of Jerusalem.
These are already in the process of being put on the western ("Israeli") side of the barrier that Israel is building in and around the West Bank.
The annexed land will include not just people and buildings, but farmland and water resources that could be a vital asset to the future Israel.
Mr Sharon's programme was strongly endorsed by Washington
An arrangement may also be devised to keep part of Hebron - Judaism's second holiest location and home to some of the most determined and hardline Israeli settlers.
And Israel may move to annexe the Jordan Valley area so it can control the entire length of the border with Jordan, from the Golan in the north to the Gulf of Aqaba.
There are several hurdles Kadima will have to clear, having already suffered its biggest body blow with the loss of Mr Sharon.
Initially, it will have to sell its plan to potential coalition partners - none of whom stood for unilateral withdrawals during the election.
The narrower-than-expected victory may mean concessions are forced on it, either from left or right.
Palestinian officials, who oppose any withdrawal that entails consolidating Jewish settlements, may find there is little they can do to stop it - especially if their obligations under the international peace plan known as the roadmap, such as disarming militant groups, remain unfulfilled.
Israel will likely brush aside Palestinian objections to new borders
Most controversial for Israel - given the hue and cry over Gaza in 2005- will be the removal of settlers living in areas earmarked for evacuation.
Kadima is trying to set the tone for this by talking about the Jews' "national and historic right to the Land of Israel in its entirety" (ie including all the occupied territories).
But its manifesto continues by asserting: "The balance between allowing Jews to fulfil their historic right... and maintaining the continued existence of Israel as the national Jewish home necessitates territorial compromise".
The government will probably start by dismantling the so-called illegal outposts - settlements not authorised by the Israeli state - as stipulated by the roadmap.
Israel appears to have already got the US administration's backing for annexing land heavily populated by Jews in the West Bank - President Bush called a return to pre-1967 borders "unrealistic" in 2004.
Kadima says the ball is now in the Palestinians' court to implement their obligations - otherwise the border-drawing will start without them.
The Palestinians' only hope is that the rest of the world will baulk at forcing them to make - as they see it - further territorial compromises, beyond an acceptance of the West Bank and Gaza as their future state.
They argue that this territory represents just 22% of the original Palestine, before Israel was established in 1948, so it already represents a significant compromise to the Israelis.