Cutting to the chase:
No one has studied and published on Euparkeria (Figs. 3-6) more than Roland Sookias and his colleagues (Sookias et al. 2014, Sookias 2016, Sookias et al. 2020). Unfortunately taxon exclusion mars all of his work (Figs. 1, 2), including his latest, otherwise terrific paper presenting close-up and µCT scans from the ten specimens found in a single locality, all attributed to Euparkeria. This paper is so rich in data, but so poor and misleading in systematics.
From the abstract:
“The archosauriform Euparkeria capensis from the Middle Triassic (Anisian) of South Africa has been of great interest since its initial description in 1913, because its anatomy shed light on the origins and early evolution of crown Archosauria and potentially approached that of the archosaur common ancestor.”
In the large reptile tree (LRT, 1714+ taxa, subset Fig. 1) Euparkeria nests far from Archosauria (= the last common ancestor of birds + crocs). Instead Euparkeria nests at the base of the Euarchosauriformes (= all archosauriforms closer to Euparkeria than to Proterosuchus and the pararchosauriforms, Fig. 1). These clades were separated in 2012 here, and that split has remained steady despite many additional taxa.

Figure 1. Subset of the LRT focusing on Archosauriformes. Clade colors match figure 2 overlay.
Phylogenetic analysis
Sookias et al. 2020 worked from a dataset in Sookias 2016. Sookias 2016 was built on the invalidated Nesbitt 2011 and Sookias et al. 2014. The Sookias et al. 2020 results are typical whenever taxon exclusion shuffles the clades, mixing unrelated taxa together. Clades nest where they do in Sookias 2020 by default. That’s how you get crocs and phytosaurs nesting together and euparkeriids arising from erythrosuchids (Fig. 2), rather that the other way around, as in the LRT (Fig. 1). We’re also wary of any cladogram that includes suprageneric taxa.

Figure 2. Sookias et al. 2020 cladogram lacks enough taxa compared to the LRT (Fig. 2) and so shuffles clades here. Here crocs nest within ‘Other Pseudosuchia’ and pterosaurs nest within Ornithodira, two clades invalidated by the LRT by adding taxa. Promoting this outdated myth of interrelationships in 2020 is not professional. Dongusuchus and Dorosuchus are know from bits and pieces of the post-crania.
Euparkeria has been studied previously,
but never so completely as in Sookias et al. 2020. As in Ewer (1965, Fig. 3) Sookias et al. present a freehand diagram chimaera skull (Figs. 4, 5) that combines data from several specimens they consider to be conspecific.

Figure 3. Previous views of Euparkeria.
Comparing a photo of the SAM 5867 specimen
to the Sookias et al. diagram may be instructive. Did they get all the details right?

Figure 4. How does the skull of the 5867 specimen of Euparkeria compare to the diagram? Here they are to the same scale. You decide on the details.
Several color photos were included in Sookias et al. 2020,
so it is surprising that their diagram lacks colors (Fig. 5 left column). When colors are added, the bones lump and separate as well as the LRT lumps and separates taxa.

Figure 5. Diagram from Sookias et al. 2020 at left. Rearranged and colored at right for ease of viewing.
Using a little DGS on a skull tracing of the SAM 4067a specimen
(Fig. 6) permits one to copy and paste elements from the left and right to create a reconstruction (Fig. 6) without reverting to the unconscious bias that attends all freehand drawings. Broom 1913 assigned this specimen to Browniella africana. Haughton 1922 considered Browniella a junior synonym and this synonymy has been accepted by all prior workers. No prior workers provided a reconstruction for accurate scoring. They just ‘eye-balled’ the roadkill skull.

Figure 6. Browniella africana, the SAM 4967a specimen attributed to Euparkeria. Images from Sookias et al. 2020 with colors and reconstruction added here.
Euparkeria capensis (Broom 1913, SAM 5867) Early Triassic, ~247 mya, 60 centimeter length is derived from the FMNH UC 1528 specimen of Youngoides (Fig. 7), a taxon ignored by Sookias et al. An unpublished paper can be found on ResearchGate.net.
The SAM 5867 specimen of Euparkeria nests between Pararchosauriformes, like Polymorphodon (Fig. 8), and all higher Euarchosauriformes like Garjainia (Fig. 9). The SAM 5867 specimen nests at the base of the Euparkeriidae, which presently include only two other tax, the SAM 4067a specimen (Fig. 6) and Osmolskina, which nest with each other (Fig. 1).

Figure 7. Youngoides romeri FMNH UC1528 demonstrates an early appearance of the antorbital fenestra in the Archosauriformes. This specimen is the outgroup to the Archosauriformes.

Figure 8. Skull elements of Polymorphodon, basal to proterochampsids.

Figure 9. Garjainia at several scales and views.
Osmolskina czatkowicensis (Borsuk-Biaynicka and Evans 2009), Early Triassic,
Browniella africana (Fig. 6, SAM 4067A) is a eurparkeriid more closely related to Osmolskina in the LRT.
Sometimes additional detail comes in handy.
And Sookias et al. 2020 provided that additional detail.
Unfortunately, without a valid phylogenetic context
you won’t know the outgroups, ingroups, ancestors and descendants of any taxon under your µCT scanner. Sometimes you need a metaphorical ‘panoramic camera’ like the LRT, for that wide gamut view that minimizes taxon exclusion.
References
Broom R 1913. On the South-African Pseudosuchian Euparkeria and Allied Genera. Proceedings of the Zoological Society of London 83: 619–633.
Borsuk-Bialynicka M and Evans SE 2009. Cranial and mandibular osteology of the Early Triassic archosauriform Osmolskina czatkowicensis from Poland. Palaeontologia Polonica 65, 235–281.
Ewer RF 1965. The Anatomy of the Thecodont Reptile Euparkeria capensis Broom Philosophical Transactions of the Royal Society London B 248 379-435.
doi: 10.1098/rstb.1965.0003
Haughton S 1922. On the reptilian genera Euparkeria Broom, and Mesosuchus Watson. Transactions of the Royal Society South Africa 10, 81–88. (doi:10.1080/00359192209519270
Nesbitt SJ 2011. The early evolution of archosaurs: relationships and the origin of major clades. Bull. Am. Mus. Nat. Hist. 352, 1–292. (doi:10.1206/352.1)
Nesbitt SJ et al. 2017 The earliest bird-line archosaurs and the assembly of the dinosaur body plan. Nature 544, 484–487.
Sookias RB, Sullivan C, Liu J, Butler RJ. 2014 Systematics of putative euparkeriids (Diapsida: Archosauriformes) from the Triassic of China. PeerJ2, e658 (doi:10.7717/peerj.658)
Sookias RB 2016. The relationships of the Euparkeriidae and the rise of Archosauria. Royal Soceity open science 3, 150674. (doi:10.1098/rsos. 150674)
Sookias RB, Dilkes D, Sobral G, Smith RMH, Wolvaardt FP, Arcucci AB, Bhullar B-AS and Werneburg I 2020. The craniomandibular anatomy of the early archosauriform Euparkeria capensis and the dawn of the archosaur skull. R. Soc. Open Sci. 7: 200116.
http://dx.doi.org/10.1098/rsos.200116
wiki/Osmolskina
http://reptileevolution.com/euparkeria.htm
http://reptileevolution.com/osmolskina.htm