Are all modern western European aristocratic families descended from one or another Germanic tribe? Did any Roman aristocratic family survive the fall of Rome and continue to today? Does this question grossly oversimplify the relationship between the Germanic tribes and Rome?
Edit: Thanks for the replies everyone!
No we can't.
Tracing one's family tree, genealogy, needs records to track relations between individual ( X's father, Y's husband, Z's brother,...Etc ). These records are various, the most common and necessary being birth, marriage, death records but others can be available such as wills, military records,...Etc
THe thing is, records for many countries began to be kept in the late 1500s ( at that date in many countries such as France, priests were asked to keep records about who they baptized, buried,...Etc. The point was to be able to keep en eye on the population so to tax them better ).
So most people can hope to trace back their genealogy to the late 1500s if they are lucky ( that the country search has such early records, that they survived the centuries,...Etc ) and good enough. Some people can be more lucky to find even older records such as wills or land property records but these are now rare and hard to find and even harder to connect to your actual ancestors with certainty.
So no, most people can only hope to be able to trace ancestors back to the 1500s ( which takes years ).
Now indeed as you said, aristocratic families had their family trees made and kept in order ( among other things ) to control who is who as well as succession and heritage matters for example. So we have early " trees " available, some more reliable than others of course. That said, even for some of the greatest families historians are not always sure on who is who or who is the father/mother of X for people having lived around the 1000 A.D. For example, who really are the first members of the great Salian dynasty ? Well it is not sure so if we had to go back to the time of the Romans it would be nothing but presomptions, full of uncertainties and mistakes ( imagine if you make a mistake early in your genealogy, such as your great grand father for example, then everything is wrong ).
There is no families existing at the time of the Roman Republic/Empire that we can assume still exists today.
One thing about genealogy that is funny though :
If you were able to go back at your generation 30, you have 537 millions ancestors and at the 35th, it's around 17 billions ancestors. You double the number of ancestors at each generation so we all at some point should descend or be related at a famous Roman or a famous tribesmen, we know it with mathematics and statistics but genealogy can't prove it for us.
Anecdote : Mathematicians say that ( you can search the exercise online ) you have 99,999996% chances of having Genghis Khan has an ancestor and only 1 chance on 24 millions of not having Genghis Khan has an ancestor
Hope this helps
Yes, but only because if you go far enough back, everyone's a relative. See /u/Georgy_K_Zhukov's post on the subject here.
No, but it is clear that many Roman families of the early successor states of Rome intermarried with Germanic aristocrats. An important problem for this kind of research is that Roman families, by the 7th century (at least in the north of Gaul, an area that is better documented in term of prosopography) had adopted Germanic names (so, to use my favourite example, a chronicler describe someone called Chramnelen as coming from the “race of the Romans”). There is, however, a series of contenders for the descent from aristocratic families; most importantly, a variety of hypotheses try to connect Charlemagne with important families of Roman Gaul, among which the Syagrii and the Ferreoli; the most likely connection is via Arnulf of Metz, Charlemagne's great-great-great-grandfather in agnatic line.
However, no-one has managed to establish safely the names of Arnulf's parents. In fact, most hypotheses would link him with the Roman world anyway: if he is the son of Ansbert the Senator, then he is obviously from Roman stock; if he is the son of Bodogisel, his mention in Gregory of Tours' work strongly supports the idea of a Roman descent. If you are interested in more detail, you can look up Christian Settipani's writings (though if I recall correctly, he does not consider Bodogisel to be a “Roman” aristocrat).
You may be interested in this previous thread: "Are there any European families that still exist today that can trace their origins to the aristocracy/patrician families of the Roman Empire?"