Most of the ones I’ve done, we take it with the dermatome, then run it through a “mesher” which cuts little slits in an alternating pattern all over it, which allows the graft to expand and cover twice the area. Then you cut a piece large enough to cover the burn or wound or w/e needs the graft, stitch if into it, then stretch the remainder out and stitch it back to the site we cut it off from.
The ones I’ve done have all been split thickness grafts where we only take the epidermis; full thickness takes the dermis and epidermis, and I assume can work the same way with a mesher.
I don’t think subcutaneous tissue is ever grafted in that context - that’s more liposuction territory, which I’ve seen that grafted in facial plastics stuff like lip restoration.