Autosomal DNA is supposed to, unlike X chromosomal DNA be passed down evenly. I say supposed to because some of my mom's results sure have me wondering when I get much larger than normal matches that go back to a 6th great grandfather.
So according to all the tables it should go roughly like this.
You get 50 percent DNA from each parent, made up of 25 percent DNA from each grandparent.
That means that each great grandparent contributes 12.5 percent to your DNA.
Each 2nd great grandparent contributes 6.25 percent to your DNA.
Each 3rd great grandparent contributes 3.125 percent to your DNA.
Each 4th great grandparent contributes 1.5625 percent to your DNA.
Each 5th great grandparent contributes 0.78125 percent to your DNA.
Each 6th great grandparent contributes 0.390625 percent to your DNA.
Each 7th great grandparent contributes 0.1953125 percent to your DNA.
And so on.
We measure matches in genetic distance (cM's) and the number of SNPs they contain. To be valid a match should contain 700 snps and be at least 7 cM long. Some of us when we are working with a known match will consider smaller matches (for me it's 5-7 cM if the number of SNP's remains high) but the odds of a match being IBS (identical by segment) is much greater than it being IBD (identical by descent). What is the difference? IBS is random and IBD is passed down.
They also have tables you can view online that give you the amount of DNA on average shared between different relatives in both percent and in cM's. Such as this one here.
According to this chart a sixth cousin on average would share 0.0122 percent of their DNA.
Observing my mother's matches, because most of my Dad's larger matches have double connections I have observed the following. She shares 0.5 percent more with her one second cousin once removed. The chart states third cousins share 0.78 percent on average, but mom's ranges go from 1.7-1.9 percent and her second cousin once removed is 2.05 percent shared. Her 3rd cousins once removed range from 0.66 percent to 1.71 percent compared to the average of 0.39 percent. Her two second twice removed matches of 0.62 percent is slightly lower than the expected 0.78 percent. She shares a whopping 0.56 percent with a Colonial 6th cousin yet only 0.52 percent with another third cousin once removed. Oddly enough on this family line, her half first cousin shares much larger matches and has smaller ones on my mother's larger ones. She also shares a whopping 0.38 percent with her 5th cousin on the 11th (see blog) with ranges on that particular match on the larger matches being from 0.38- 1.0 percent DNA that is no closer than her 6th grandfather.
So what am I implying?
I am implying that we don't get exactly half of each grandparent's DNA. That just like X DNA it mixed together on each chromosome so that it is possible to share almost 1 percent DNA with a 6th cousin that shares only one set of MCA. (which according to how DNA is passed down is impossible). It doesn't mean you don't get a bit of DNA from each line, you just get uneven bits of DNA I think, which is why mom's Collins matches are small and her Hager matches are larger for her and vice versa for her Hager cousin.
No proof, just my observations, and maybe some food for thought.