I did try the search-box, but didn't see answers to my question, so here we go!
So Wall Of Stone requires "adjoining rock surfaces" for the conjured wall to be anchored to. What constitutes such a surface? Can my wizard carry around a brick to use as an anchor-point? Can he cast Transmute Mud To Rock on a patch of ground to create a stone pad and then anchor the Wall of Stone to that surface? I'm not at all adverse to carrying a waterskin to make a large mud-puddle for my engineer to work from. I need a baseplate, but the wording of Wall of Stone pretty plainly requires an existing stone structure, rather than allowing my wiz to cast Wall to create a really nice horizontal slab on the ground as a foundation, thus the "carry a brick" part of the equation.
What about Rampart? It reads, "You create a massive rampart of hard-packed earth and stone 5 feet thick." Would that count and allow Wall of Stone to anchor to it?
It must be "solidly supported" by existing stone. My interpretation: the structural stability must be greater than that provided by the Wall of Stone itself. So, say a giant came that was able to pick up the amount of stone that is generated by a Wall of Stone - he should not be able to move the wall once it is firmly anchored, even though he would be able to pick it up without its anchor.
So, I would rule that a brick is not sufficient, as it provides no structural integrity not already inherent to the Wall of Stone itself.
Another way you could think about it - if you removed the ground underneath the Wall of Stone, the anchor should be able to hold the weight of the wall.