Tiarella L.
As currently circumscribed Tiarella is a genus with three species. Two are native to North America (T. cordifolia L. and T. trifoliata L.; Jog 2009), one to Asia (T. polyphylla D. Don; Pan & Soltis 2001). Previous treatments, including those refering to the genus in cultivation, usually applied a narrower species concept. Miller (1995) and Jäger & al. (2008), for instance, accepted six species that are cultivated as ornamentals. In addition to those currently accepted: T. wherryi Lakela, T. unifoliolata Hook. and T. laciniata Hook. All are now subsumed under T. cordifolia and T. trifoliata, either as mere synonyms or at a lower taxonomic rank (variety).
The most widespread species in cultivation probably is Tiarella cordifolia. It has been recorded as an escape in Belgium.
Literature
Jäger E.J., Ebel F., Hanelt P. & Müller G. (eds.) (2008) Rothmaler Band 5. Exkursionsflora von Deutschland. Krautige Zier- und Nutzpflanzen. Springer Verlag, Berlin: 880 p.
Jog S. (2009) Tiarella. In: Flora of North America Editorial Committee (eds.), Flora of North America, vol. 8. Oxford University Press, New York-Oxford: 114-116. [available online at: http://www.efloras.org/florataxon.aspx?flora_id=1&taxon_id=132985]
Lakela O. (1937) A monograph of the genus Tiarella L. in North America. Amer. J. Bot. 24: 344-351.
Miller D.M. (1995) Tiarella. In: Cullen J. & al. (eds.), The European Garden Flora, vol. 4. Cambridge University Press, Cambridge: 281-282.
Pan J. & Soltis D.E. (2001) Tiarella. In: Wu Z.Y. & Raven P.H. (Eds.) Flora of China 8. Science Press, Beijing & Missouri Botanical Garden Press, St. Louis: 344-345. [available online at: http://flora.huh.harvard.edu/china/PDF/PDF08/TIARELLA.pdf]
Reveal J.L. (1991) Typification of the Linnaean species of Tiarella (Saxifragaceae). Phytologia 71(6): 479-482. [available online at: http://www.biodiversitylibrary.org/item/47401#page/53/mode/1up]
Savile D.B.O. (1973) Vegetative distinctions in Canadian species of Mitella and Tiarella. Canad. Field-Nat. 87(4): 460-462.
Soltis D.E. (1980) Karyotypic relationships among species of Boykinia, Heuchera, Mitella, Sullivantia, Tiarella, and Tolmiea (Saxifragaceae). Syst. Bot. 5(1): 17-29.
Soltis D.E. (1982) Heterochromatin banding in Boykinia, Heuchera, Mitella, Sullivantia, Tiarella, and Tolmiea (Saxifragaceae). Amer. J. Bot. 69(1): 108-115.
Soltis D.E. & Bohm B.A. (1984) Karyology and flavonoid chemistry of the disjunct species of Tiarella (Saxifragaceae). Syst. Bot. 9(4): 441-447.
Soltis D.E. & Bohm B.A. (1985) Chromosomal and flavonoid chemical confirmation of intergeneric hybridization between Tolmiea and Tellima (Saxifragaceae). Revue canadienne de botanique 63(7): 1309-1312. [available online at: https://www.researchgate.net/profile/Douglas_Soltis/publication/23716250...
Taylor R.J. (1971) Biosystematics of the genus Tiarella in the Washington Cascades. Northwest Sci. (USA) 45(1): 27-37.
Taylor R.J. (1971) Intraindividual phenolic variation in the genus Tiarella (Saxifragaceae); its genetic regulation and application to systematics. Taxon 20(4): 467-472.