The Proto-Indo-European phonetic reconstruction is strongly tied to the past: acceptance of traditional distinction of three series of velars is still widespread today in handbooks and articles on the parent language and on early Indo-European proto-languages alike.
Direct comparison in early IE studies, informed by the centum-satem isogloss, yielded the reconstruction of three rows of dorsal consonants in Late Proto-Indo-European by Bezzenberger (1890), a theory which became classic after Brugmann included it in the Second Edition of his Grundriss. It was based on vocabulary comparison; so e.g. from PIE *km̥tóm ‘hundred’, there are so-called satem (cf. OInd. śatám, Av. satəm, Lith. šimtas, OCS sto) and centum languages (cf. Gk. -katón, Lat. centum, Goth. hund, OIr. cet).
To explain the phonetic differences between both groups, a series of labiovelars *kw, *gw, and *gwh, and another of palatovelars *kj, *gj, and *gjh, were reconstructed along with the plain velar series. These sounds underwent a characteristic phonetic change in both dialectal groups, whereby three original “velar rows” became two in all attested Indo-European dialects. After that original belief, then, the centum group of languages merged the palatovelars *kj, *gj, and *gjh with the plain velars *k, *g, and *gh, while the satem group of languages merged the labiovelars *kw, *gw, and *gwh with the plain velars *k, *g, and *gh.
The reasoning for reconstructing three series was very simple: the easiest and most straightforward solution for the parent PIE language was that it had all three rows reconstructed for the proto-languages, which would have merged into two rows depending on their dialectal (centum vs. satem) situation – even if no single IE dialect shows three series of velars. Also, for a long time this division was identified with an old dialectal division within the Indo-European-speaking territory, especially because both groups appeared not to overlap geographically: the centum branches were to the west of satem languages. Such an initial answer should be considered unsound today, at least as a starting point to obtain a better explanation for this ‘phonological puzzle’ (Adrados, Bernabé, and Mendoza 2010).
Many Indo-Europeanists still keep a distinction of three distinct series of velars for the parent Indo-Hittite language (and mostly unchanged for the Late Proto-Indo-European stage), although research has constantly supported that the palatovelar series were most likely a late phonetic development of certain so-called satem dialects. This model was formulated quite early in the development of the velar series by Antoine Meillet (1894), and has been followed by many linguists since then, such as Hirt (1899), (1927), Lehmann (1952), Georgiev (1966), Bernabé (1971), Steensland (1972), Miller (1976), Allen (1978), Kortlandt (1980), Shields (1981), etc.
The general trend is to reconstruct labiovelars and plain velars, so that the hypothesis of two series of velars is usually identified with this theory. Among those who support two series of velars there is, however, a minority who consider the labiovelars a secondary development from the pure velars, and reconstruct only velars and palatovelars, such as Kuryłowicz (1935), already criticised by Bernabé, Steensland, Miller, and Allen. Still less acceptance had the proposal to reconstruct only a labiovelar and a palatal series by Magnusson (1967).