Hansel, there is no way to recieve factual statistics on the illegal sources of firearms. One could only guesstimate. You would need to take explore every account of what makes a firearm illegal and where it came from. Now add it all up. It’s quite impossible. I would gladly give up my shotgun and rifle if EVERYONE would give up their’s. Wishfull thinking. 
Drugs are good, that’s why I smoke Marijuana.
Here’s the bottom line, as I see it. If guns were completely banned, anyone who wanted one whould still be able to get one easily enough. A black market would exist. If the black marketeers could not get legal guns here in the US to sell to illegal purchasers, they would import guns from other countries and / or manufactor them in clandestine factories. If a demand exists, someone will supply it. Govt. cannot succeed in either banning guns or controlling them. It is just as futile as prohibition and the war on (some) drugs.
Bantmof pointed out that “A law cannot ‘make something difficult’. All it can do is punish action after it happens.” Hardly anyone grasps this simple, very true, fact. Unfortunately.
Laws do not have the power to change people’s behavior. Period.
I figure Ill just leave this little input of mine for you to consider-1) why are switchblades illegal? I have one but I dont even like it because I have legal knives that I can open faster than it.2)Guns (and anything else) can be bought and sold at Flea Markets. Techically (since you did not go through the gov’t to get to it its illegal.3)What difference does it make if the guns are illegal or not to the people who USE them? I forget the statistic is , but its pretty small - USUALLY guns are used for hunting or sport only. It really is the rarity for someone to use it to kill people. And if they get rid of them all together people will resort to Swords, Bows, Crossbows, etc and ruin those for the rest of us too.(ok so it wasnt short but I think I have a good point or two)
This is a ridiculous oversimplification: of course they do. That’s not to say that passing a law causes a sea change in the behaviour of the masses, but the passing/existence of laws always has some determinative effect.
Accountants receive changes to tax laws every year, and alter their bookkeeping accordingly. Lawyers follow cases that set precedent, and argue differently in court.
More fundamentally, gun manufacturers stop manufacturing certain firearms or parts, or mass produce them before the effective date, because of laws about firearms. People smoke in public areas in New York, Los Angeles and Toronto less than before because of non-smoking laws.
It’s not merely the suggestion of punishment that changes people’s behaviour. Laws can dictate requirements for certain acts, and those requirements are followed to a greater or lesser degree. As I said before, a law can make something difficult by altering the behaviour of those whose co-operation you require to commit an illegal act.
If laws really don’t affect behaviour at all, why not do away with them?