Nuclear DNA tests strongly suggest that Denisovans and Neandethals diverged quite some time after they, collectively, diverged from H.s.sapiens. (Subsequently in this piece I will use “human” as a synonym for H.s.sapiens for brevity and elegance.)
Despite this, Y and mt-DNA comparisons tended to show that Neanderthals and humans are more closely related than are Neanderthals and Denisovans, or humans and Denisovans.
As older specimens were analysed, it became clear that at some point, the mt-DNA of Neanderthals was completely replaced by a human strain, probably between 500000 and 250000 years ago.
https://www.nature.com/articles/ncomms16046
A couple of years ago it also was shown that the Y-DNA was also replaced with a human strain. (Y-DNA is apparently less well preserved or harder to sequence, because there are fewer dot points than for mt-DNA).
https://www.science.org/content/article/how-neanderthals-lost-their-y-chromosome
This is interesting to think about, for me, for a couple of reasons.
Firstly it is a reminder about how different mt- and Y- DNA inheritance are from the nuclear DNA that gets shared through sexual reproduction. mt and Y have family trees like bacteria. A parent has many children but each child has only one parent. So while an interbreeding event can introduce some new traits to a population, it can’t result in a wholesale eradication of the population’s nuclear DNA information, but it can result in the eradication of all the previous mt and Y DNA information: wiped, completely lost, such that the mt-Eve or Y-Adam were, suddently, outsiders.
Secondly the mt-DNA story might tell us a little about the relationships between us and the Neanderthals. It’s been known for ages that there were interbreeding events between the two groups, but it might for instance have resulted from fleeting liaisons: a human and a neanderthal had sex, the female became pregnant and gave birth, but the two basically remained in their own groups afterwards. But the fact that human mt-DNA entered (and indeed eventually dominated) the Neanderthal pool means that the female human must have joined the Neanderthal group, had daughters that also bred with Neanderthals etc.