FACTBOX: Israel leadership vote and what follows

(Reuters) - Israel's ruling Kadima party votes in three weeks for a successor to Prime Minister Ehud Olmert, who has said he will step down because of corruption investigations.

The following are mechanics of the primary and scenarios for how the winner may -- or may not -- become prime minister.

* On Sept. 17, Kadima's 70,000 members head to polling stations at 22 party offices to cast ballots.

* For now there are four candidates, though some may yet drop out: Foreign Minister Tzipi Livni, Deputy Prime Minister Shaul Mofaz, Internal Security Minister Avi Dichter and Tourism Minister Meir Sheetrit.

* Polls indicate Livni will beat Mofaz into second place, but such surveys have been wrong in the past on party primaries.

* The winner needs 40 percent to avoid a two-person run-off a week later. Results are expected the day after voting.

* The new Kadima leader will not automatically become prime minister. Several steps must follow:

-- Olmert must resign, which he has pledged to do. Once he does, however, he remains caretaker premier until his successor, or someone else, has formed a new government -- a process that may happen almost instantly but could take months.

-- To form a government, the new Kadima leader will need a formal mandate to do so from President Shimon Peres. He can take up to 14 days to grant it.

-- The nominated future premier then has 42 days to conclude coalition agreements with several other parties -- failure could technically lead to Peres mandating someone else to go through the same process. Further failure would trigger an election.

* Kadima has 29 of 120 Knesset seats and depends on the 19 seats of the Labour party, led by Defence Minister Ehud Barak, for the core of a coalition that also includes religious parties and others. Though polls indicate that Labour would fare poorly in an election, if Barak or others refuse to follow the new Kadima leader, then parliament, which reconvenes on October 26 could vote to dissolve itself. An election must be held within five months. More typically it would be in early 2009. The next election is not currently scheduled until spring 2010.

* An alternative scenario in the event of the new Kadima leader being unable to form a government would be for Peres to mandate the leader of another party to try to form a government. This seems unlikely at this stage, however. The right-wing Likud opposition, led by Benjamin Netanyahu, is tipped by polls to be the biggest party after any general election and so is unlikely to help form a new government in the current legislature. And Barak cannot become prime minister in the present parliament because he does not hold a seat in it and cannot secure one.

*Under all the above possibilities, Olmert could stay on as caretaker prime minister until such time as a new government was formally sworn in. However, he could also ask to step aside, in which case Livni as his current deputy would become caretaker.