I went to a session that David Reich talked about his research on the Denisova during the American Society of Human Genetics annual meeting in Montreal last month and I had a chance to talk to him briefly after the session.
These articles are the results of collaboration of leading scientists, David Reich (Harvard University), Svante Paabo (Max Planck Institute), Mark Stoneking (Max Planck Institute), Montgomery Slatkin (University of California, Berkeley). It is really a dream team of scientists.
The most important finding from this project is that they found the evidence of ancient admixture between the Denisova and anatomically modern human from Southeast Asian, New Guinea, Australia, and Oceania. They estimated that the Denisova contributed up to 7% of genetic materials of modern people from the areas.

Considering that the Denisova was found in southern Siberia, the mechanism of interaction between the Denisova and modern human is difficult to understand. From reading the articles and talking to David Reich, I am guessing that they considered many scenarios of interaction, but based on their available data, they believe the interaction took place in Southeast Asia.
Another important thing from this project is that now we have better understanding of the relationship between the Denisova and Neanderthals and between the Denisova and anatomically modern human. The Denisova is more closely related to the Neanderthals than modern human, and they shared an ancestor about 640,000 years ago. Modern human shared an ancestor with the Denisova and Neanderthals about 804,000 years ago. The phylogenetic tree constructed from whole genome data was very different from the tree based on mtDNA genome data (See here).

Ancient genome data from archaic human is still limited, but current data favors the Multiregional model and suggests that both Denisova and Neanderthal (go here for the Neanderthal genome) contributed genetic material to the gene pool of anatomically modern human. If we have a lot more ancient genome data, we may find evidence of substantial genetic contributions from archaic human, completely rejecting simplistic view of Out-of-Africa model.
[...] added DNA material to, for example, Melanesians. In Reich, et alii, papers summarized in “Evidence of ancient admixture between the Denisova and anatomically modern human from Southeast Asia…,” estimated that the Denisova contributed “up to 7% of genetic materials of modern [...]