Mongols: Temujin (who wasn't called Genghis yet at that time) dies early in 1200. The Mongols and other Steppe People fall apart, fighting among themselves instead. Temujin's son Ogadai manages to unite them for a second time, fights the Kara-Kitai, the Tangutes / Hsi-Hsia and even challenges the Choresmians, who still are victorious under their Shah Jalal-ad-Din Manguberdi I. After Ogadai's death, the steppe people fall apart again.
Muslim world: Choresm conquers Baghdad, makes the Caliph its puppet, extends its influence down to the Mediterranean. The Shi'ites stay stronger. Assassins survive. Rum-Seljuks kick out Byzantium / Nikaia from Asia Minor. Mamluks come to power in Egypt, conquer Crusader States in Palestine.
Eastern Europe: Hungary controls Bosnia, Serbia and OTL Romania. Volga Hungarians go to Hungary proper, convert to Christianity. Bulgaria stays more stable. Nikaia can reconquer Constantinople eventually, but has to agree on a union of the churches, and is dangerously weakened. The Teutonic Order subjugates Prussians earlier, conquers Lithuania. Vladimir-Suzdal expands at the expense of Volga Bulgarians. Kara-Kitai attack the Kumans, but the latter under Baibars can defend successfully.
Western Europe: Poland is (mostly) reunited, a new king is crowned. Hungary expands into Austria for short time, but is beaten back by Otakar Przemysl, who doesn't inherit Bohemia ITTL, but can keep Austria in the family and is elected king of the Holy Roman Empire. The Przemyslid lands are split between two lines of succession. Other than that, no changes.
America, Oceania, sub-Saharan Africa: No changes.
Muslim World: Choresm falls apart after Shi'ite revolts, Persia becomes independent. The Rum-Seljuks conquer Syria, Balcans.
East Asia: Hong China makes all of East Asia its sphere of influence, sends Treasure ships to Seljuks, clashes with them.
Eastern Europe: Russians start to expand into Siberia, Ukraine. Religious schism drives Vladimir-Suzdal and Kiev further apart from each other. Teutonic Order loses its first war.
Western and Central Europe: France wins second and third Aquitainian War, kicks out England from its soil. England conquers Scotland, Castille takes Portugal, and both unite to form the Quadruple Monarchy. Territories of the church in the HRE seized, leading to Twenty-Year War. All Italian states except Savoy, Venice and Florence lose independence. Netherlands, Switzerland become stronger. Bohemia becomes a theocracy.
Atlantis (America): Europeans start trading tobacco and pelts. Denmark, Scotland, Florence, Sweden, Braunschweig-Lüneburg, England, France and Castille found first colonies (although Scotland loses them again). Mayapan destroyed.
Atlantis: All Western European countries take some Caribbean islands. The Quadruple Monarchy expands greatly, but is restricted in the Great Occidental War by France, which allies with Mexico and Tawantinsuyu (the Inca), who survive as empires, despite being struck hard by European diseases. The Mississippi and Hudson Bay area become part of the French sphere of influence.
Western and Northern Europe: In the Quadruple Monarchy, the king takes control over the church, founding the Occidental church with some new laws. The churches are reunificated however after the Occidental War, which also leads to the independence of Scotland-Ireland under the quasi-legendary Prince Alasdair, who later also becomes king of Scandinavia. Aragon divided between France and Castille.
Central Europe: HRE makes reforms, elects French kings Holy Roman Emperors. Florence expands, getting Rome, Naples, Sardinia. Hungary is resurrected by the French, who also conquer the Bohemian theocracy. Venice, Württemberg-Austria and Bavaria make the "Alliance des Alpes" with France.
Muslim world: After initial successes (conquest of Vienna, the Marches, Kipchaks pay them tribute) the Seljuks are defeated several times by the Christians, losing many lands to the Europeans. They also get more and more trouble with the Dvoryans (OTL Cossacks) in the Ukraine.
Atlantis: French Louisiane mostly divided between Germans, Italians and English after the anti-French War. Mexica subjugated by Spaniards. Braseal and Argentine colonized by England. Russians take Alyeska and the West Coast down to San Francisco Bay.
Europe: Triple Monarchy of England-Castille-Portugal falls apart. Englands suffers a Civil War that brings Stafford dynasty to power. During this power vacuum, France greatly expands its influence over most of Europe under absolutist François IV. In the great anti-French War their empire breaks together, and Scotland and Portugal lose independence. Hungary practices religious tolerance.
Russian lands: Siberia becomes the independent republic of Novorossiya, has good relations with China. Kipchak lands north of the Black Sea conquered by Russians, formed into the new "Dvoryan republics". Science and humanities blossom in Novorossiya.
Muslim world: Seljuks still lose against Europeans, but achieve some victories in the second half of the century. Persia conquers Oman, Delhi.
East Asia: Independent nations between China and Russians conquered by the latter. Hong China loses power and influence, at the expense of the "rim people" (Nipponese, Koreans, SE Asians). Western Europeans enter the scene.
Rest of the world: Songhay empire in Africa becomes stronger. French visit and ally with Ethiopia. Many Portuguese go to the "ship settlements" in the sea of Guinea. Swedes reconquer Australafrica.
Atlantis: Germans, Italians, Spaniards and English extend their settlements until reaching the Rockies, where they meet the Russians who have spread from Alyeska. After the French Republican Wars, Italy annexes the French colonies and some Spanish islands. German Atlantis declares independency after their home country Denmark-Braunschweig ceases to exist.
Europe: Sweden-Netherlands gives more power to the parliament. After its setback in the anti-French War, France can restore its position somehow. After the death of king Charles X, the country has the estates debate for years about the right heir, which leads to the people declaring a republic when they see that a king-less government is perfectly possible. In the following French Republican Wars, France achieves dominance over Germany and Iberia. For quite some time, general Boulanger governs the country with dictatorical power. Pope loses more influence to the kings, has to flee after the changes in France first to Spain, later to Britain.
Russian lands: The invention of the telegraph spreads from Russia to other Eurasian nations. Vladimir-Suzdal is defeated and divided by Novorossiya and South Russia (Kiev-Chernigov + Dvoryan republics). Serbia and Bosnia gain independence after centuries. Novorossiya expands into Finland, Prussia, Central Asian steppe.
Muslim world: Shi'ite Persia still becomes stronger, pushes Seljuks back. "New Seljuks" try to reform their state. France again tries to occupy the Sinai, for a connection to India. Egypt becomes independent.
East Asia: France founds the short-lived Indochinese League. Hong China is attacked by its former tributaries, losing some provinces in the South. General Lin Xiaolong uses the opportunity to take power, founding Ming China. Spain gains influence in Nippon.
Atlantis: Canada revolts successfully against Britain. Anti-slavery movement starts in the German lands and Canada. New Roman empire conquers Inca lands and former Spanish colonies. British colonies in the south divided between New Rome and Germans.
Europe: France has more and more problems keeping Germany and Spain under control. Germany itself, Switzerland and the Dutch kick out French occupation. Monarchy abolished in Nassau and Hungary. Italy becomes the New Roman empire. Britain goes through two revolutions, becoming first republican and then Socialist.
Russian lands: Russia invades Poland, Hungary and Bohemia, until the other powers start the anti-Russian War.
Muslim world: Bulgaria and Pontus are lost to the Russians. Egypt is conquered by Italy. The Seljuk sultanate becomes a republic. Choresm conquered by Novorossiya. Independent state of Judea founded.
East Asia: Ming China first reconquers the old empire, but faces problems when population grows out of control. New Rome starts hiring Indians as auxiliaries.
Rest of the world: Antipodia becomes the Irish-speaking state of Tir Tairngire, where the pope takes his seat.
Atlantis: Russia restricted to a few coastal places and Alyeska. Northern California becomes independent after the Gold Rush. Braseal also gains independence from New Rome.
Europe: New Rome conquers first the Iberian peninsula and later most of France, creating a few new kingdoms. Germany gains Prussia, Lothringen and adds Poland, Bohemia, Hungary and later Scandinavia to its sphere of influence. Socialists try to make revolutions on the continent, but are defeated by German troops.
Russian lands: After losing the anti-Russian War, Russia reforms. Later they expand into China, Central Asia, make the Black Sea a Russian lake.
Muslim world: The remaining Muslim powers of Choresm, Persia and the Seljuk republic are crushed by the great powers.
East Asia: Ming dynasty falls when the growing population joins the Orthodox-influenced "Society of brotherly love", until a general restores order. India becomes dependent on the New Roman Empire. Canada expands its influence in SE Asia.
Rest of the world: Germany makes most of sub-saharan Africa its protectorate, starting with Guinea, Zanzibar and Australia (OTL South Africa).
Rest of the world: