DISCLAIMER Read this paragraph before the rest of the post below: Any time I use the term "counterpoise" in this post it is referring to the traditional meaning of the term as stated in the first quote below from an old ARRL Antenna Book. I also quote a few people on this forum who are very knowledgeable. I am not saying they don't know what they are talking about when it comes to antennas, I am simply using their use of the word in question as an improper use as per the historical definition of the term as it relates to antenna engineering. The definition I use is based on my own research into the historical meaning of the word in question. I also invite you do do your own research on this subject as I would love to have a technical discussion on what counterpoise meant and what it should mean today.
I'll start by quoting a source and go from there...

This is in my opinion the best description of what a counterpoise is (or at least was at the time this book was written) that I have come across. It is packed with information, including but not limited to:
It is a form of capacity ground.
It is beneficial when an extensive ground system is not practicle.
It is beneficial in rocky or sandy soil where it will not be easy to lay out a buried ground system.
The bigger it is the better.
The shape does not matter.
The number of wires is not critical.
Cross connected wires are allowed (and recommended).
No benefit in extending the radius past ½λ.
No relationship is necessary between the λ and the length of the wires.
The intention is to have the counterpoise act as a pure capacity rather than having pure resonance effects.
More wires are better, minimum number of wires depends on the size and frequency of the counterpoise.
It is a good plan to design the wire layout to minimize resonance.
It is a good idea to raise a counterpoise above (earth) ground as if it is to close it will have more losses.
I also want to point out that this is in the 160 meters section of the book, which is dealing with antennas that have to, by necessity, be very large because of their much lower frequencies. A shortened quarter wave 160 meter antenna that was shortened to the equivalent of a 3 foot cb antenna would still be longer than a 5/8 wave cb antenna.
Not picking on anyone but just the first few quotes I found doing a search on this forum.
Found this in your "Marconi comparing New Top One vs. Old Top One" thread. The antennas in question are rarely close enough to the earth that their radials would act as as a capacity with the earth below. The maximum effective height for a counterpoise at cb frequencies which I believe is around two feet off of the ground. As you go above that the shear size that would be required at the frequencies used would make it more of an artificial ground plane, not a capacity with the earth below. Also, the direct connection of a ground wire to a ground rod would also nullify any chance of it being a counterpoise (not specifically stated in the quote, but a commonly used setup for these types of antennas I think). I have read nothing anywhere that specifically states that a counterpoise has to have horizontal wires, however, I feel the angled radials of these antennas, even if they were close enough to the earth to have a capacity with the earth, would be far less than an optimal setup to have a capacitance with the earth.
And the reply.
These quotes are from within the "New antenna from Sirio Gain-Master" thread. They are referring to an elevated radial system (or perhaps the lack thereof) and the effects of the mast below. This misuse of the term is within the limits of a category that is by far the most commonly used today. If the term would find itself having a new definition for the current era of antennas this is close to what I think it would be. However, there are other examples. Being an antenna on a mast, any radials would be far to far above the earth to have a capacity with it, and thus it does not match up with aforementioned source/definition.
From youtube:
Video 1
This is by far the second most common misuse of the term. One common misconception of a counterpoise being anything connected to the shield of the coax, which is not necessarily the case. This also assumes that coax will be in use, however, the term counterpoise, as it is referred to with antennas, predates the existence of coax feed lines.
Video 2
This is the third category, and is far less common than the other two mentioned above. All they are doing here is increasing the conductivity of the earth below a horizontal antenna. They also call it a ground plane later in the video which is also technically incorrect (as my understanding of the term "ground plane" would apply). I am not saying this can't be an effective option/upgrade for people with horizontal antennas, but it is not a counterpoise.
Does this help Marconi?
The DB