There are two kinds of skin grafts, as I understand it. One is called a full-thickness graft and includes both the epidermis and dermis, while a thinner split-level is sort of the variable graft that doesn't include both layers of skin. If you're getting a skin graft, depending on what doctors determine, having a thick graft is a desirable thing as the post-healing graft will maintain smoother skin qualities. With all great sounding deals, a full-thickness graft needs a lot more favorable conditions for it to heal correctly. On the bright side, it is usually used to graft on smaller areas... which is a silver lining right? You've been burned or have otherwise hurt your largest organ, but if you get a full-thickness graft at least that means the area needing a graft is smaller.
Again, as I understand what I was told, for large areas that have been damaged the skin can be meshed. And, yes, it looks exactly like you might expect. There are different tools that can sort of fishnet stocking your skin graft.
This is what one of the mesher tools looks like. Less high
tech than one would image.