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Good question. Length to diameter ratio can affect it some. Not only is the resonant length shorter for a fat conductor the impedance will be effected a bit too due to the difference in ohmic losses. I suspect this may be part of the reason why we see a certain value for a 10m antenna and yet a different value for a 2m antenna with the same size material used. There is a difference in terms of wavelength and unless even wire size is scaled the outcome would be different. The material used will affect the outcome as well. Copper, aluminum, and stainless steel all have different electrical properties so that will make a bit of a difference as well. How far the feedpoint is from the groundplane will make a difference too as the ground lead has to be factored in. Something I don't think is being taken into account either is that that figure of 35 ohms, and that is a "nominal" 35 ohms not a hard and fast definite value, (sort of like 50 ohms coax being somewhat near 50 ohms but not exactly)  not only assumes a perfect groundplane but if memory serves me correctly it also assumes that perfect groundplane is in free space which eliminates any coupling effects to anything other than the groundplane. Antenna installations are so varied that it is impossible to say something will be X value all the time everywhere in all cases. IMHO worrying about whether it is truly 35 ohms or 27 ohms or 41 ohms is simply a waste of time. The fact remains that it must be matched to 50 ohms for most applications and using the nominal value of 35 ohms is as good a starting point as any.

Just as a real example, back in 1986 I moved an AM transmitter site to a new location. The old site being encroached upon by developments and had the original 1948 tower which was a short top loaded affair that was unstable electrically with changes in the weather. I had a 160 foot steel tower installed with a 24 inch face at the new location on a piece of prime dyke land with very good conductivity. The frequency was 1450 KHz making the 160 foot tower a ful 1/4 wave. The ground system consisted of 120 radials spaced equally around the base and each radial was a 1/4 wavelength of 10 gauge bare solid wire. The radials were flat with the exception that about 1/4 of them sloped downwards slightly for about half their length due to terrain. Directly at the base of the tower was a 20 foot by 20 foot ground mat made from 6 gauge stranded wire with the wires  running in both directions and spaced one foot apart and silver soldered with Silfoss wherever they crossed. This was done to maintain a more stable ground in the immediate area of the tower. When all was said and done and the tower self impedance measured we ended up with 38 ohms R and just a few ohms of reactance.This was before the electrical cables and clearance lights were added as well as the Austin toroidal lighting transformer at the base. I merely present this as a real world example of an installation and what the results were. Nothing more.

BTW when I said "And yet there are countless examples all over the internet on countless sites that agree with what I said. Gee ....go figure." it was not meant to be against anything you said but merely an observation of facts. I believe we are on the same wavelength to use a very bad pun.