There are some officials in the Israeli government, the defense establishment, and, certainly, on the Right who won't shed a tear if Mahmoud Abbas, widely known by his nom de guerre Abu Mazen, will indeed go through with his threat to resign from his position as head of the Palestinian Authority.Yisrael Beytenu chief Avigdor Liberman on Tuesday already issued an acid-tongued statement on that possibility. Abbas on Tuesday once again repeated his pledge not to stand as Fatah's candidate for re-election as the head of the Palestine Liberation Organization. For months, the 80-year-old Abbas has been threatening to quit out of sheer exasperation. It's not just his age. Abbas has despaired of any hopes of advancing the peace process together with the Netanyahu government. He has also grown disappointed with the international community, which is not cooperating with his wish to force the UN Security Council to recognize a Palestinian state.The world has lost interest in the Palestinian question, an issue that has faded from the global agenda. The boycotts of Israeli goods produced in West Bank settlements have also proven to be insufficient. The unbridgeable gaps between Abbas and Hamas have also been a key, contributing factor to his despair.Senior officials in Fatah responded to Abbas' statements by saying that as far as they are concerned, he is still their leader. But there are also those in Fatah and the PLO who will be happy to see the old man step down.Abbas rivals accuse him of imposing a dictatorial regime that brooks no opposition, rewards cronies, tolerates corruption, and spends wastefully, as illustrated by recent reports that the Palestinian leader was building a $13 million private compound.Nobody is irreplaceable. "The graveyards are full of indispensable men," so goes the famous saying. Abbas is also a leader devoid of charisma and pizzazz, certainly when compared with the revolutionary aura that surrounded his predecessor, the colorful Yasser Arafat.The question of who will be Abbas' successor sooner or later has preoccupied the defense and intelligence communities in Israel. A number of names have been bandied about, yet nobody in Israel can say for certain who will be the next leader of Palestine. Not even the Palestinians know the answer to this question.Marwan Barghouti, who is serving multiple life sentences in prison due to his involvement in planning terrorist attacks that killed Israelis during the second intifada, has been mentioned as a possible replacement.There have been calls in recent years for Israel to release Barghouti, a man who is considered a charismatic leader who enjoys the backing of the Palestinian "street." Saeb Erekat and Muhammad Dahlan have also been rumored to be in line to take Abbas' place.Whoever succeeds Abbas will be a figure of the so-called second generation, that group of men who lack the prestige that was earned by the founding members of Fatah over 50 years ago. With Abbas' anticipated departure, a chapter in Palestinian history comes to an end. It is difficult to foresee how the next chapter unfolds.Yes, Abbas is viewed as a hesitant, weak, and indecisive man who at the last minute walked away from the most generous peace offer ever presented by Israel. That was during Ehud Olmert's tenure as prime minister.It should be said that Abbas did genuinely believe in the two-state solution. Unlike Arafat, who was wont to say one thing yet do another, Abbas shed his allegiance to "armed conflict," or - as Israel prefers to look at it - terrorism.Future Israeli governments - including those on the Right - will miss Abbas. Israel is liable to regret its decision to refuse to advance the peace process and engage in serious negotiations. It is obvious to all that Abbas' successor will have to be more extreme and intransigent, which means that the chances for peace - such as they are - will shrink even further.Ultimately, Israel may find itself in a predicament in which the Palestinian Authority will be dismantled and Hamas will enter the vacuum. Perhaps this is what Israel's right-wing leadership really wants.