As Ariel Sharon lies in a hospital bed, many wonder how his successor will handle the Palestinian question.

One of the great ironies of Sharon’s career is that he became identified as the best hope for a solution to the Palestinian conflict. This was a man who was demonized by Arabs and who disdained negotiations with the Palestinians. But he also was the man who unilaterally withdrew troops and Jewish settlements from the Gaza Strip.

The Bush administration stood back and let him guide its policy on the peace process, hoping he would make further withdrawals from the West Bank. Few believe the next Israeli leader will take such a bold risk. Prospects for movement on the Palestinian issue are now in a coma.

No one would have predicted that Israelis would turn to Sharon for a plausible solution to the Palestinian problem. As a military man, he was known for his willingness to tolerate Palestinian civilian casualties during strikes on Palestinian targets. On his watch, Lebanese Christian militias massacred Palestinians in the Sabra and Shatila refugee camps of Beirut in 1982.

Sharon was the architect of Israel’s plan to populate the West Bank and Gaza with Jewish settlements. He used to carry laminated maps of the Jewish settlement grid he had instituted on the West Bank, eager to tell listeners why each colony was essential to Israeli security. The grid was meant to prevent the formation of a coherent Palestinian state.

As Israeli prime minister, he kept expanding the settlements. His aides suggested that Palestinians could have a ministate made up of chunks of West Bank land located between settlement blocs; these Palestinian cantons would be linked by tunnels and bridges. This was not a solution that could work.

Sharon was unwilling to negotiate the boundaries of a state – especially when the obstreperous Palestinian leader Yasser Arafat was still alive. Instead, he began building a fence that would separate Israel from the West Bank and incorporate key settlement blocs into Israel proper.

But something seemed to have changed in Sharon’s thinking over the past year. Perhaps he recognized what those in the Israeli center and left repeatedly had warned of: Palestinian demographics threatened the survival of Israel as a Jewish state.

Unless Israelis gave up the West Bank and Gaza, Palestinians soon would compose the majority of the population in greater Israel. If they were denied political rights, the world would begin comparing Israeli rule of Gaza and the West Bank with South African apartheid.

No doubt the demographic threat motivated Sharon’s dramatic decision to withdraw from Gaza and dismantle the settlements he had championed.

No one knows whether Sharon would have made further withdrawals. Most Palestinians believe the Gaza pullout was meant to cement Israel’s hold on the West Bank. Indeed, one of Sharon’s key aides, Dov Weisglass, said as much in an interview with Ha’aretz in October 2004.

But last week – before Sharon’s stroke – the Israeli paper Ma’ariv ran a fascinating piece claiming that Sharon intended to make a dramatic move on the West Bank after this March’s elections.

The article said Sharon intended to pull back from all but 8 percent to 12 percent of the West Bank and evacuate dozens more settlements in return for an agreement with the United States recognizing Israeli sovereignty over the entire Old City of Jerusalem. Such an agreement, Ma’ariv claimed, also would include U.S. rejection of the “right of return” to Israel by 1948 Palestinian refugees.

By negotiating this accord with the Bush administration, not the Palestinians, Israel would effectively turn custodianship of the Palestinians over to the United States.

Needless to say, the Palestinians rejected such an idea. I can’t believe the Bush team would have accepted it either. Nor do we know whether the Ma’ariv article was “spin” or reflected real plans by Sharon.

What we know is that none of Sharon’s potential successors is likely to propose any such bold move. His deputy, Ehud Olmert, might want to emulate Sharon but won’t have his boss’ strong public backing. Nor is it certain how well Sharon’s new centrist party, Kadima, will do in the March elections without him.

Meantime, the Palestinian leadership is divided and beset by factional violence. The Islamist group Hamas, which opposes Israel’s existence, will do well in March elections. This makes Israeli-Palestinian negotiations even less likely.

Sharon’s boldness might have galvanized the Palestinians into coherence. With him gone, there is no such goad. Nor does the Bush administration have a policy of its own for the post-Sharon era.

It’s hard to see who will jump-start the Israel-Palestinian peace process now.