Europeans crusading in the Middle East praised the Mongols (under the Prester John myth) as they crushed their muslim enemies.

Meanwhile Europeans prayed for a savior against the other branch Mongols spreading across Russian lands.

It'a been 20 years but I seem to remember it was the Mongols in the north of Europe that secured tributary vassals and opted not to return to Mongolia for electing a new Khan and the lineage of Jochi became rather independent. They moved south around the Black and Caspian Seas instead.