1200: Temujin dies by an accident. Since his four sons (Jochi, Chagatai, Ogadai, and Tolui) are still too young (they're between 10 and 15 years old now), he has no clear successor. Enemies of Temujin, like his former friend and blood brother Jamukha Gurkhan, some of the clans and people he defeated and some people who're simply ambitious try to use the situation, and the people Temujin already united fall apart. Some of Temujin's "Dogs of war" (Subodai, Chilaun, Jelme and Borchu) and his family are still willing to fight to preserve his heritage, but for the beginning his dream has suffered a setback. The following years are filled by infighting between the various steppe tribes and people, with too many battles and changing alliances to mention them.
1205: Ogadai, the most talented and charismatic of Temujin's sons, is old enough to fight by himself for his father's dream, but he still needs the support of his elder brothers and the supporters of his father. He'll never be able to be a ruler as strong as his father.
(as OTL) Muhammad has conquered all of Great Seljuk and declared himself Shah.
1207: Jochi (who is suspected that Temujin isn't really his father) is killed by his brother(?) Chagatai.
1210: After Chagatai dies in a fight, Ogadai finally becomes the accepted Khan of the Mongols. Now he can continue the suspended work of his father to unite the steppe people. He'll take longer for that than his father and won't be 100% successful, though.
1212 (as OTL): Shah Muhammad defeats the Gur-Khan Kutluk and conquers the lands of the Kara-Kitai, to whom the Choresmians once had to pay tribute.
1213: Ogadai defeats the Merkites. Now he plans to fight the Tatars who once killed his father's father, but the attacking Keraites force him to postpone the plan. To make things worse for him, the subjugated people often rebel because he makes them introduce the Mongols' Code of Law.
1216: Keraites defeated by Ogadai. Now he's ready to fight the Tatars.
1217/18 (as OTL): Shah Muhammad plans to attack the Caliphate of Baghdad, but too many of his soldiers die in a blizzard in the mountains, so he has to postpone the attack.
1221: After many bloody fights, the remaining Tatars join his horde.
1222: Shah Muhammad dies, is succeeded by his son Jalal-ad-Din. (OOC: There's not too much known about him; IOTL, he managed to save himself by jumping from a dangerously high place into a river after having lost against the Mongols; even Genghiz is said to have been impressed by his courage, so I'm giving him the benefit of doubt and make him a courageous warrior ITTL.) Jalal-ad-Din reigns a great empire, consisting of today's Iran and all the -stans. However, this also means he has to care for various groups trying to rebel against him. Being a good warrior, he eventually succeeds and keeps the empire together.
1225: Naimans defeated.
1227: Uighurs defeated. Ogadai notes that they use writing, which the Mongols don't know yet. He thinks it would be a good idea to use this new knowledge.
Since 1229: Ogadai starts writing down the Yassa, the old and new Laws of the Mongols.
1230: Jalal-ad-Din has consolidated his empire.
1230-32: Ogadai leads the united steppe people against the Tangutes / Hsi-Hsia. Their country is overrun, many of their villages burnt down and their people enslaved. The Mongols don't have the necessary technics to storm their cities, though. OTOH, they manage to capture the secret of gunpowder. Ogadai wants to take the cities by besieging them, but after two years the other Mongols think they have a) spent enough time here and b) there's not enough left to loot for the effort. So Ogadai leaves the country for a high tribute (mostly camels). The Hsi-Hsia empire has suffered extremely under the occupation, and won't recover from it.
1233: Jalal-ad-Din demands formal recognition from the caliph in Baghdad. When the caliph Al-Mustansir rejects his claim, the Shah proclaims one of his nobles caliph and marches towards Baghdad to depose the caliph.
1234: Kara-Kitai defeated by Mongols. Ogadai now reigns the biggest (if sparely populated) empire on the planet.
1235-38: Various campaigns in Southern Siberia against the Kirghiz and Tuvans.
1236: Choresmians take Baghdad, topple the old Abbasid caliph. Al-Mustansir is imprisoned, some of his relatives flee to Egypt and the lands of the Rum-Seljuks.
1239: Choresm Shah Jalal-ad-Din marries his daughter Khadiya to his puppet Caliph.
1240: After a governor of the Choresm Shah insults Ogadai by killing his diplomats, he decides to attack Choresm. In the battle near the city of Otrar, Ogadai and Jalal-ad-Din meet each other. The attack of the Mongols is successful at first, but the courageous Shah manages to collect his men and prevents a catastrophy. The situation at other frontiers is also indecisive.
1241: Ogadai dies. His son Guyuk (not the same-named from OTL) is the designated successor, but some of his family members won't accept him, and some of the allied non-Mongol people (Tatars, Kara-Kitai, Naimans, Merkites) wish for more independency. Jalal-ad-Din can use the situation for a counter-attack and drives the Mongols back behind Lake Balchash. He also manages to get the secret of gunpowder, which will become important in the future. The steppe people once again fall apart, not to be united at least for decades, waiting for another strong leader.
For the first repercussions, see also: