Frequent museum-goers are probably aware that most of those mounted skeletons that you see at museums aren't one individual - they're composites (like the metoposaurid above at the American Museum), sometimes of multiple individuals found together and sometimes of multiple individuals found apart. The fossil record isn't kind to most skeletons, and 99.99999% (more or less) of all fossils are just isolated bits. The good news is you can often cobble together the many bits to make a collection of bits, which maybe looks more like a skeleton, but the bits need to fit. Think about it like fashion (this is not my expertise, don't crucify me): you can usually make many different combinations of clothes that work, but they need to fit - you probably don't pair winter coats with speedos (though this would be done in California if anywhere). Not only that, but you probably can't (or wouldn't) use clothes from when you were a teenager as an adult. Of course, maybe your teenage fashion sense was super cringy, and that's why you won't do it, but one of the other reasons might be that your clothes (even your favourite hoodie from that concert in 11th grade) from back then don't fit. It's the same idea when making a composite fossil - the bits all have to fit, and that means they have to come from individuals that were about the same size.
A very quick and dirty primer on branchiosaurids
Branchiosauridae is an old family, named in 1879 by Czech paleontologist Antonín Frič (often written as Fritsch in English) for the eponymous Branchiosaurus, named a few years prior in 1876. Members were historically referred to as 'branchiosaurs' although the proper derivation is 'branchiosaurids,' as is now used. The majority of branchiosaurids were named in the late 1800s or the earliest 1900s, but they were often tossed into Branchiosaurus as a wastebasket taxon; the present recognized diversity is the result of extensive revision in the past few decades by a number of European workers, chief among them Jürgen Boy, Ralf Werneburg, Andrew Milner, and Rainer Schoch. Note that both regular Google and Google Scholar insist that you must be searching for Brachiosaurus when you search for 'branchiosaurs' or 'Branchiosaurus'...evidencing the deep conspiracy to keep dinosaurs at the top of the internet food chain!
Branchiosaurids are known only from the Carboniferous and the Permian (though Tungussogyrinus is maybe from the earliest Triassic) and almost exclusively from Europe; it may be that higher-elevation lakes found in Europe at the time were more conducive to these aquatic taxa (both for living and for preservation) compared to the inverse distribution for terrestrial amphibamiforms (common in N. America, rare in Europe). Branchiosaurids, like terrestrial amphibamiforms, were quite small, most with skulls less than 3 cm long, and they're some of the best examples of soft tissue preservation among temnospondyls with many specimens showing the outlines of the body and gills. Also unlike most temnospondyls, some branchiosaurids, particularly Apateon, are known from hundreds of specimens, and those are just the known ones (many show up on fossil-selling websites out of reach of academic paleontologists). They're typified by various anatomical features, including the separation of the palatine and the ectopterygoid from the maxilla (see Leptorophus from Schoch, 2014 below), reduced vertebral count, and a maxilla sometimes separated from the quadratojugal, creating a gap below the orbit (see Tungussogyrinus from Werneburg, 2009 above).
So how do branchiosaurids fit into the points that I talked about at the start? Well, one of the longstanding ideas to explain the absence / scarcity of juvenile temnospondyls is that rather than not having them preserved, perhaps we do actually have various growth stages of temnospondyls – we just haven't properly recognized them for what they are. Branchiosaurids are the group that was most widely hypothesized to possible be these unrecognized larval forms because they fit several criteria for what we expect from larvae based on what we knew (know) about modern amphibians: small, aquatic, and retain external gills.
A review of the evidence now available indicates...that the branchiosaurs are feebly ossified and, for the most part, immature representatives of the various groups of the Labyrinthodontia. - A.S. Romer (1939)
The famous American paleontologist Alfred Sherwood Romer was one of the first to publicly question the validity of branchiosaurs, which were at the time placed in a now defunct order called Phyllospondyli that largely encompassed small forms of questionable larval status. Romer argued that what were called 'branchiosaurs' were in fact the missing larval forms of already known Paleozoic temnospondyls like the eryopoid Actinodon and the peculiar form Stegops (which remains somewhat indeterminate to date). He called particular attention to the fact that branchiosaurs typically were found in low-energy lake settings that seemed intuitive as the breeding / early life habitat of large temnospondyls. Invoking a hypothesis of fairly drastic changes (like what we see in modern amphibians), he reasoned that there could have been some drastic changes in the temnospondyl skull that would explain some discrepancies. Of course, under that rationale, almost anything of size 'X' could hypothetically turn into something else of size 'Y,' and we now know that most temnospondyls don't undergo very drastic changes or metamorphosis. Despite his stance on branchiosaurids, Romer recommended that "Branchiosauridae" be maintained as a dumping ground for larval forms and that the various branchiosaur genera be used as "form genera" along the lines of how paleobotanists apparently do for dissociated plant parts (I have no clue if this is still done; I don't work on plants...). Subsequent paleontologists adopted Romer's views of branchiosaurs until they were challenged in a series of papers by German paleontologist Jürgen Boy in the 1970s (most of the papers are in German, but the abstracts / summaries sometimes come in English as well), leading to the recognition of Branchiosauridae as a valid family of neotenic temnospondyls (explaining why they looked like larval forms) with distinctive taxonomic features and their subsequent addition to Dissorophoidea. For those unfamiliar with the term 'neoteny,' it refers to the retention of juvenile features (like external gills in amphibians) in adults that results from a retarding of development. The modern axolotl is a classic example of neoteny. Since then, branchiosaurs have become an excellent case study for examining heterochrony (changes in developmental events' timing and duration) and metamorphosis in temnospondyls (e.g., Fröbisch & Schoch, 2009; Schoch & Fröbisch, 2006; Schoch, 2010).
Although we recognize now that branchiosaurids don't represent larval Paleozoic temnospondyls, it's possible that the true juveniles of terrestrially capable dissorophoids might look a lot like the adults of small aquatic dissorophoids like micromelerpetids and most branchiosaurids. The available evidence does support this at present, although preserved specimens can be differentiated. But this is the fossil record, so not all of the features used to identify those small groups are always going to be preserved or exposed in a specimen, and closely related groups would be inferred to have similar developmental pathways such that if say...one was just truncated, rather than drastically altered, there might be some confusion? The below diagram is from Andrew Milner's 2018 paper revising trematopids (the big long-snouted dissorophoids) in which he also commented a bit on the historical conundrums and various nuances that we can use to differentiate adult micromelerpetids and branchiosaurids from larval olsoniforms (trematopids + dissorophids). (The text is probably too small to make out some of the features, but they include things like vertebral count, branchial dentition, proportions of some bones, and skull profile).
Some other short notes on branchiosaurids. Because they're so common in Europe, there's been a lot of studies beyond just description and taxonomy for this group. Examples include colouration of the skin (Werneburg, 2007), cannibalism (Witzmann, 2009), and cool x-ray stuff (Sanchez et al., 2010). There's a lot of really cool data out there on skeletal formation, development, and other things that you can only test with big sample sizes. I haven't gone much into branchiosaurids because I am less familiar with them myself, but they are worth checking out if you can get over Google's attempts to autocorrect your search!
About the blog
A blog on all things temnospondyl written by someone who spends too much time thinking about them. Covers all aspects of temnospondyl paleobiology and ongoing research (not just mine).