The Azhdarchoidea (Unwin 1995) is a putative clade of derived pterosaurs created to unite the Azhdarchidae (Quetzalcoatlus and kin) with the Tapejaridae (Tapejara and kin). Characters uniting taxa within this putative clade include: 1) Orbit positioned lower than dorsal rim of nasoantorbital fenestra; 2) Manual 4.2 more than a third shorter than m4.1.
Is Azhdarchoidea a Valid Clade?
The tall antorbital fenestra either unites Chaoyangopterus with Huaxiapterus (Fig. 1) or this trait developed by convergence. Manual 4.2 is indeed only 2/3 the length of m4.1 in Chaoyangopterus, but m4.2 is a bit too long (82%) in Huaxiapterus. Manual 4.2 is likewise less than 2/3 of m4.1 in the tiny pterosaur, n42. In Tapejara m4.2 is also a bit too long, but 2/3 the length of m4.1 in other tapejarids, such as Tupuxuara.

Figure 1. Click to enlarge. Putative members of the Azhdarchoidea include Chaoyangopterus and Huaxiapterus (red arrows). The larger study found no clade uniting just the Azhdarchidae and the Tapejaridae. Instead n42 was found to be basal to azhdarchids and Germanodactylus cristatus n61 was found to be basal to tapejarids.
Similarities
It’s easy to see several similarities in azhdarchids and tapejarids, including the elongated metacarpus, the depth of the suborbital jugal, the depth of the mandible at mid length, and the short m4.4. Unfortunately many other distinctions separate these two taxa in the larger pterosaur tree.
Distinctions
In dorsal view, the azhdarchid mandible has parallel sides ending in a rounded tip. In tapejarids and germanodactylids the mandible is sharp with a tooth at its tip. A posterior cranial crest is present in tapejarids and germanodactylids, but not in azhdarchids. The antorbital fenestra extends for 2/3 of the rostrum in tapejarids and germanodactylids, not in azhdarchids. The number of dorsal vertebrae is smaller in azhdarchids and protoazhdarchids. The pedal phalangeal ratios are more similar in protoazhdarchids and azhdarchids than in tapejarids. Similar pedal phalangeal proportions unite germanodactylids and tapejarids.

Figure 2. Left to right, Eopteranodon, Wellnhofer's No. 13 and Aurorazhdarcho, sisters that nest far from the Azhdarchidae.
A Basal Azhdarchoid?
Aurorazhdarcho (Frey, Meyer and Tischlinger 2011, Fig. 2) was promoted as the basalmost azhdarchoid. Unfortunately no phylogenetic analysis was published. Here, in the large pterosaur tree, Aurorazhdarcho nested with other stork-like pterosaurs, Eopteranodon and Eoazhdarcho, at the base of Nyctosaurus + Pteranodon, distinct from both the Tapejaridae and the Azhdarchidae.
The Benefit of a Larger Family Tree
Here again the benefit of a larger family tree permits an entire suite of traits, from head to toe, define cladistic relations. More taxa is the key to understanding, as any paleontologist will tell you, except when dealing with pterosaur relations [sarcasm]. Not sure why other paleo scientists refuse to expand their taxon list to match mine.
As always, I encourage readers to see specimens, make observations and come to your own conclusions. Test. Test. And test again.
Evidence and support in the form of nexus, pdf and jpeg files will be sent to all who request additional data.
References
Frey E, Meyer CA and Tischlinger H 2011. The oldest azhdarchoid pterosaur from the Late Jurassic Solnhofen Limestone (Early Tithonian) of Southern Germany. Swiss Journal of Geosciences 104 (Supplement 1): 35–55. doi:10.1007/s00015-011-0073-1.
Unwin DM 1995. Preliminary results of a phylogenetic analysis of the Pterosauria (Diapsida: Archosauria); pp. 69-72 in Sun, A. and Wang, Q.-Y. (eds.), Sixth Symposium on Mesozoic Terrestrial Ecosystems and Biota, short papers. China Ocean Press, Beijing.