Here are the study results about chubby vs. skinny grafts.

Poorer growth rates when using thin grafts compared to “chubby” graft
Dr. Seager, Dr. Beener, Dr. Beeher, Dr. Reed and Dr. Raposio each conducted studies to compare the results of chubby and thin grafts.

All studies show that compared to the chubby grafts, the growth rate of the skinny graft is decreased 15% to 33%. So far we haven’t heard any report indicating that the thin graft’s growth rates are better.