In the start of the previous century Schwartz (1926) and later Bjork (1955, 1960) investigated the relationship of head posture and craniofacial growth. When A. Bjork retired from the professorship of Copenhagen orthodontic department, Beni Sollow with his interest in cephalometrics continued the research on the field. Prof B.Sollow conducted a series of observational studies concerning head posture and growth (1976, 1986, 1992)
S.D.Springate of the Eastman Dental Institute, has published at the current issue of the European Journal of Orthodontics, a study that tries to put all those key articles under a critical eye and re-investigate the exact relationship of head posture and craniofacial growth.
Here is the link to the abstract of the study.
The main weakness of B.Sollow's studies as pointed by the author of the above study, is the fact that posture is assessed only prior growth and not afterwards. The reasoning B.Sollow used was that since he had two variables with a relation with each-other, the one that occurs earlier is the one responsible for the outcome of the later. With that argumentation the posture, that is there earlier in time, is the one effecting the craniofacial growth that follows.