Permanent mandibular molars (PMMs) exhibit two main roots (mesial and distal), but numerical variations are not uncommon. Differentiation of the main roots may be incomplete, which results in a one-rooted PMM (Carlsen, 1990). Also, two other developmental processes yield a PMM with more than two roots: division of the mesial root and formation of additional or supernumerary roots (Carlsen and Alexandersen, 1990, Carlsen and Alexandersen, 1991). Radix entomolaris (RE) and radix paramolaris (RP) are anatomical terms used to denote a supernumerary root on the lingual or buccal side of the main roots, respectively. The first description of RE was provided by Carabelli (1844), but the term itself was introduced by Lenhossék (1922). The first description and naming of RP were done by Bolk (1915). Both supernumerary roots can be separate or non-separate in relation to the main roots (Carlsen and Alexandersen, 1990, Carlsen and Alexandersen, 1991). In the morphologically most stable first PMMs, three-rootedness is synonymous with the presence of a RE on the distolingual aspect, whereas supernumerary roots and bifurcated mesial roots both also occur in the more variable second and third PMMs (Schulze, 1987). Moreover, they exhibit variation in RE locations, including distolingual, midlingual, and mesiolingual variants (Carlsen & Alexandersen, 1990).

RE and RP have numerous clinical implications. Their identification may be difficult on a periapical radiograph because of buccolingual superimposition with the main roots (Calberson et al., 2007). Those that remain undiagnosed even after direct examination of the pulp chamber floor result in missed canals with an increased risk of endodontic treatment failure (Karabucak et al., 2016). Moreover, they frequently exhibit pronounced curvatures and/or divergence in relation to the main roots (Carlsen and Alexandersen, 1990, Carlsen and Alexandersen, 1991), which poses a risk of causing a ledge, root perforation, or instrument separation during the endodontic treatment (de Pablo et al., 2012, Yu et al., 2012). The advised procedures for safe instrumentation of this severely curved canal include an extension of the conventional access cavity outline, adequate coronal flaring for straight access, and the use of NiTi files to maintain original canal curvature (Abella et al., 2011, Calberson et al., 2007, De Moor et al., 2004). Furthermore, the increased root furcation complexity in the affected teeth can contribute to a local progression of advanced periodontal disease, as has been shown in comparative studies of two-rooted and three-rooted first PMMs (Goh and Ong, 2019, Huang et al., 2007). Not surprisingly, epidemiological data indicates that three-rooted first PMMs are lost in significantly younger patients than their two-rooted counterparts (Gu et al., 2010). Curvature and apical gracility of supernumerary roots frequently complicate tooth extractions (Loh, 1990). Additionally, the successful accomplishment of apical surgery on three-rooted first PMMs requires a modified protocol with different surgical access (Zhang et al., 2017).

Research on three-rooted first PMMs has a long history and has provided extensive data on their prevalence worldwide (de Pablo et al., 2010, Scott et al., 2018b), which is not so for the second and third PMMs with supernumerary roots. There are several reasons that these teeth have remained outside the research focus. First, they less frequently require endodontic treatment than first PMMs (Castellucci, 2004); second, they do not represent key dental elements for population comparisons in dental anthropology (Scott & Irish, 2017); finally, they exhibit a more variable root morphology that may be difficult to interpret from conventional 2-dimensional images, e.g., panoramic and periapical radiographs (Schulze, 1987). In the previous two decades, cone-beam computed tomography (CBCT) surpassed conventional radiography in terms of its ability to visualize the external and internal root morphology (Ring & Ring, 2017). In recent years, there has been an increasing number of CBCT studies evaluating the root and root canal morphology in second PMMs (Alazemi et al., 2023, Buchanan et al., 2023, Kim et al., 2016, Martins et al., 2017, Pawar et al., 2017, Plotino et al., 2013, Saber et al., 2023, Senan et al., 2021, Shemesh et al., 2015, Silva et al., 2013, Yang et al., 2022, Zhang et al., 2011), but third PMMs remain understudied (Jing et al., 2023, Priyank et al., 2023, Somasundaram et al., 2017). Moreover, only one study statistically analyzed the concurrent presence of supernumerary roots in adjacent first and second PMMs (Song et al., 2010).

This study is based on the retrospective analysis of CBCT scans in a sample from Slovenia and aims to investigate: (1) the frequency of PMMs with supernumerary roots, (2) the patterns of unilateral and bilateral concurrency, and (3) the external morphology of the affected teeth.