The antorbital fenestra is THE classic trait marking the traditional Archosauria (Archosauriformes). However, the large reptile study produced four clades with an antorbital fenestra. Here they are:
Figure 1. The antorbital fenestra in four reptiles. Chroniosuchus represents the chroniosuchids. Cosesaurus represents the Fenestrasauria, which includes the pterosaurs. Parasuchus represents the Pararchosauriformes. Proterosuchus represents the Euarchosauriformes, which includes the dinosaurs, crocs and birds. Each antorbital fenestra appeared individually, unrelated to and by convergence with the others. Virtually all present studies do not recognize this.
There are several characters that most paleontologists consider originated only once. Among them is the antorbital fenestra, an extra hole in the skull between the naris and orbit. The present large analysis (Figure 2) recovered a single tree in which the antorbital fnenestra appered four times: 1) in the Chroniosuchia (basal lepidosauromorph); 2) in the Fenestrasauria (which also includes the Pterosauria — and the antorbital fenestra may also extend to Jesairosarus and the Drepanosauridae); 3) in the higher Pararchosauriformes (proterochampids, phytosaurs and chanaresuchids); and 4) the Euarchosauriformes (including crocodilians and birds and several prehistoric clades including dinosaurs).
Figure 2. Click to enlarge. The four appearances of the antorbital fenestra in the Reptilia.
Antorbital fenestra means “the window anterior to the orbit [or eye socket]”. In certain taxa (euarchosauriforms and pararchosauriformes), the antorbital fenestra is deeper than the surface of the skull and lies in a bony depression called the antorbital fossa. Chroniosuchids and fenestrasaurs do not have this trait. Certain taxa have reduced the antorbital fenestra or have it entirely closed over.
The Function of the Antorbital Fenestra
Various hypotheses have been advanced regarding the function of the antorbital fenestra: 1) as a housing for a gland; 2) as a housing for pterygoideus musculature; 3) as a housing for an air-filled sac. Unfortunately most of the reptiles that ever had an antorbital fenestra are now extinct and in all living crocodilians the antorbital fenestra is closed over. However in birds the antorbital fossa houses a large air-filled diverticulum of the nasal cavity—the antorbital sinus. Thus the antorbital fenestra is associated with the nasal passage and likely housed an air-filled sac, thereby lightening the skull’s weight. Taxa that exhibit modifications of the nasal passage (adding a secondary palate, for instance) show reduction or loss of the antorbital fossa/fenestra. Rabbits, deer and certain extinct horses likewise have/had tiny antorbital fenestrae. Details and more references on the various hypotheses of origin and function can be found in Witmer (1987).
References:
Witmer LM 1987. The Nature of the Antorbital Fossa of Archosaurs: Shifting the Null Hypothesis. Fourth Symposium on Mesozoic Terrestrial Ecosystems, Short Papers Ed. by P.J. Currie and EH. Koster. online pdf
The Pterosaur Heresies 