Thanks for the comments, and just to answer your points...
1) Cheers
2) You are indeed right in saying Tamerlane invaded northern India, but the maps I am basing it upon are from when the Mongol empire was at its greatest extent. Jusing Tamerlane's time (early 1300s) much of the empire was split up and other regions had become independant, so it would be a more fragmented map.
3) As for Tibet, they did attack (although not a full scale invasion) but you are right in saying they left Tibet alone for the most part. It was, however, a dependant region still within the empire just as much as many other areas. The Tibetan leader was subservient to the Mongols. It was also important in that Tibet brought Buddhism to the Mongols. This quote from wikipedia might explain it better:
In 1240, the Mongols marched into central Tibet and attacked several monasteries. Köden, younger brother of Mongol ruler Güyük Khan, participated in a ceremony recognizing the Sa-skya lama as temporal ruler of Tibet in 1247. The Mongol khans had ruled northern China since 1215. They were the emperors of the Yuan Dynasty. Kublai Khan was a patron of Tibetan Buddhism and appointed the Sa-skya Lama his "Imperial preceptor," or chief religious official. Tibetans viewed this relationship as an example of yon-mchod, or priest-patron relationship. In practice, the Sa-skya lama was subordinate to the Mongol khan.
And for more detailed info check out this essay:
http://www.tibet.com/Status/mongol.html
Thanks again for the comments, and as a general notice I must let everyone know I'm pretty busy at the moment but I'll try and iron out the wall at the weekend if at all possible.