I think you are thinking too globally. The theory I am familiar with, and the one that is most agreed with by scientists, is this:
Neanderthals were a separate species that evolved in Europe from Homo heidelbergensis. They were closely related to Homo sapiens, and there may have been some interbreeding, but not enough to change the DNA of mankind. Neanderthal country included Europe, the Middle East, Russia, and Central Asia. We either outcompeted them, they died from climate change (the decline of forests in Europe at the time), or diseases brought over from our species killed them.
The last known hold out for the Neanderthals was the Iberian peninsula.
http://en.wikipedia.org/wiki/Neanderthals#Habitat_and_range
its just a wikipedia article, but it talks about how the last fossils are mostly found in iberia and gibraltar. i'm sure it can lead you to some other sites with more information
I truly doubt disease killed off the Neanderthal. All seriously infectious diseases, save TB, Malaria, Herpes, and some Eukaryotic pathogens (which were for the most part left in Africa), did not emerge until after the Agricultural revolution.
Crossbreeding was not likely a cause of extinction. Heard of Grolar bears? Well around 2 million years ago, polar Bears and grizzly bears diverged. If they mate, their offspring, the Grolar bear is perfectly fertile, able to breed new pizzly bears.
H. Sapiens and H. Neanderthalis were not seperated long enough to make sterile offspring.
Considering how rabbity Homo was over all, I think Humans could successfully breed with the almost alien H. Erectus, possibly Austrailopithecus
What probably killed them off was competition with Humans. We have no Kosher impulse, as demonstrated by the rape of Mauritius.
If they perhaps lived where the modern taiga is, they could farm/hunt reindeer, where very few humans live even today.
http://news.mongabay.com/2010/0301-hance_polarbears.html said:One of the most well-known animals, the polar bear, is a newcomer on the world stage, according to research published in the Proceedings of the National Academy of Sciences. By studying the DNA of an ancient polar bear jawbone uncovered in 2004 in Norway scientists have for the first time pinpointed the time when the polar bear split from its closest relative, the brown bear.
"Our results confirm that the polar bear is an evolutionarily young species that split off from brown bears some 150,000 years ago and evolved extremely rapidly during the late Pleistocene, perhaps adapting to the opening of new habitats and food sources in response to climate changes just before the last interglacial period," says Charlotte Lindqvist, PhD, research assistant professor in the UB Department of Biological Sciences and lead author on the paper.
Here's a BBC articlehttp://en.wikipedia.org/wiki/Neanderthals#Habitat_and_range
its just a wikipedia article, but it talks about how the last fossils are mostly found in iberia and gibraltar. i'm sure it can lead you to some other sites with more information