Batu means 'firm' and amongst his brothers, the sons of Jochi, he was well adapted to become Great Khan.
But in the end of the day, because Jochi was not recognised as a full blood relative by his brothers, he was very well aware that this would unlikely become a reality.
The 'golden' Horde was named after the colour of his Tent and spread almost towards the boundaries of France. Since Batu found it difficult to reign the western territories from the banks of the Volga, it is almost certain he would have founded a court in the West and I assume that this was Sarajevo, in the Balkans.
The last remark is not without meaning. The Eagle as symbol of the Byzantine Eagle also became that of the Russian Horde and Roman Empire and is symbol over kingship. It may very well be that Frederick II inspired Batu Khan towards a whole new vision with regard to the place of Europe in the Great Horde, which may very well be one of the reasons Batu Khan did not proceed further than the Balkans.
|Tartar map of Golden Horde|
But, we have already seen, that there was little hope of a son of Jochi becoming the Great Khan. Even when he is almost given the opportunity by some of the sons of Genghis Khan - merely because of his merits - he at the last moment declines and favours Mongke to become Great Khan.
After that, the common theory is the Batu stayed in service of the expansion of the Mongol Empire in the East, but that seems rather out of character. Batu had installed Mongke as first to remain himself the stronger second. It is much more likely that - inspired by Frederik II - Batu Khan started to work on a whole new vision for the West, which he regarded as his legitimate domains. Here his already established place as 'king maker' would take an entirely new direction.
Batu Khan, would take the in the meantime Latin Empire of Byzantium, more westwards and would become the Pope of the West, not yet even from the Italian Rome, but from the Balkans. From there he would proclaim an entirely new vision. He would conquer Europe spiritually and use for its purpose its own established form of Catholicism. He would do that, so in the long run he would by himself outflank the ranks of the Great Khanate, the Russian Horde.
|Innocent III Lord of the World|
But for now the western Papacy of Innocent III would remain in the Balkans and only through the period of Avignon become established in the Italian Rome.
Batu Khan was the third in line from Genghis Khan, the Lord of the World, and as Pope Innocent III he became his replacement for the West. This would make the western Papacy Batu Khan's scheme to get even with the Great Khanate and the humiliation of Jochi by the hands of his brothers.