I would not claim that most do so but the real fact is we do not know exactly how much to attribute to straw purchasing (which includes those actually trafficking them), stolen firearms, etc. When you are dealing with surveys on illegal activities, without outside verification of responses, you get a probability range such as betting odds rather than hard numbers. Thus, you can go with hard numbers such as federal prosecutions for firearms trafficking.
You have to add that percentage of about 20-25 percent to that of the underground market which is about 43 percent to that from family and friends. The Pittsburg study cited above indicates that only about 58 percent of claimed stolen firearms were reported to the police which indicates that at least some percentage of the respondents replying to the survey probably illegally transferred firearms to a prohibited person. http://www.socialmedicine.info/index.php/socialmedicine/article/download/852/1649
Useful summary: "Given that 79% of perpetrators are connected to firearms for which they are not the legal
owner, it is highly likely that a significant amount of theft or trafficking is the source of perpetrators’ firearms."
My suspicion is that the underground market varies depending on rural versus urban, high gun control requirements versus lower ones by state, the relative presence of gangs and their composition, and so forth.
Here is one example from LA, "Many "crime guns" move quickly from legal sale into criminal use. Research has shown that one of every five guns that is used in a crime in Los Angeles moves very quickly from its initial, legal sale into criminal use." Source: Bureau of Alcohol, Tobacco, and Firearms, Crime Gun Trace Reports (2000): National Report, Washington, D.C.: U.S. Department of the Treasury, 2002.
A later, more in depth RAND study of firearm trace software in LA, indicates this,
"When we restrict the geographic scope further and include only those instances in which the last legal purchaser lived within a 4.5-mile radius of the target area, we find that more than one-third (35 percent) of all purchasers resided within this area. Though we are unable to determine how the firearm came into the possession of the illegal possessor (e.g., stolen, nonreported transaction, straw purchase), this clearly demonstrates that much of the illegal firearm market is “local.” The locality of the market applies both to the nearness of the FFL that last legally sold the firearm to the last-known legal purchaser (who did not possess the firearm at time of the recovery).
These analyses indicate that, in a one-year period, 35 percent of the 989 guns recovered (that were purchased in that year) were not in the hands of the original purchaser—yet the purchaser lived within the 77th Street area. We know little about how guns are transformed from legally purchased firearms to crime guns. Theft, straw purchasing, gifts, and undocumented sales are all possible. The interagency working group hypothesized that these methods of entry into the illegal firearm market were prime candidates for disruption, because they begin with a legal purchaser. Since federal law prohibits felons and other potentially dangerous individuals from purchasing firearms, the original purchaser must have only a minor or no criminal record and, therefore, can plausibly be deterred from transferring the legally purchased firearm to another." https://www.ncjrs.gov/pdffiles1/nij/grants/241135.pdf
A common remedy in social science, when you are dealing with large discrepancies of estimates of likelihood in your variable, such as straw purchasing, you conduct a meta analysis to establish some sort of range for the variable. What we know is that straw purchasing is greater than zero percent if nothing else because of a few prosecutions. A more reasonable assertion is to investigate firearms that have a quick turnaround between the original legal sale and the firearm showing up in illegal activity. This shortens the timespan for theft likelihood versus a thirty year old weapon which are often difficult, if not impossible to trace due to ownership changes.
The LA studies listed above indicated that between 20-35 percent of LA firearms recovered that were involved in crimes demonstrate this sort of short term turnaround for the study area which was the South Central section of LA. Whether this is generalizable to other places is unknown.
