Otaitense Orange / Red Lime / Otaheite Acidless Rangpur Lime - European plant haul (14) 

This variety is known by a number of synonyms. Citrus Otaitense, Otaitense Orange, Red Lime, Othaheite Rangpur Lime.
The following is a brief description I have found online -
"Usually referred to as the Otaheite orange, this fruit should be properly regarded as an acidless or sweet form of the Rangpur and therefore should probably be called the Otaheite Rangpur. The tree is similar to the common Rangpur but less vigorous and hence dwarfed. It is almost thornless and the purple coloration on the new shoot growth is more intense. Likewise, the fruit is similar but somewhat smaller, more commonly necked, contains fewer normal seeds (often none), and is insipidly sweet from lack of acid.
Since an acidless form of the Rangpur is known in India, this fruit doubtless originated there. However, the first known reference to it (Risso and Poiteau, 1818-22, p. 66) described it as Citrus otaitense, a small orange from Otaite (Tahiti) brought to Paris from England in 1813. How or when it reached the United States is not known, but it was listed as a potted ornamental in the 1882 nursery catalog of R. J. Trumble of San Francisco, California (Butterfield, 1963). Easily propagated from cuttings, as are all the Rangpur, it is extensively grown in the United States as a potted ornamental, primarily as a winter house plant. Several unnamed clones are recognized.
Fruit small to medium in size, variable in form but mainly depressed globose to round or broadly obovate; sometimes with furrowed collar or low neck; often with short nipple partially or entirely surrounded by a shallow furrow. Rind color yellowish to reddish-orange; thin, and moderately loose, with surface minutely pitted and smooth to slightly rough. Segments 8 to 10, loosely adherent; axis large and hollow at maturity. Flesh orange-colored; tender, juicy, and strongly acid. Seeds fairly numerous, small, highly polyembryonic, and with light green cotyledons. Fruit holds on tree for a long period.
Tree usually vigorous and productive, medium-sized, spreading and drooping, with slender twigs, comparatively few and small thorns; foliage dull-green and mandarin-like, and new shoot growth lightly purple-tinted. Flowers small and mandarin-like and buds and petals deeply purple-tinged. Hardy to cold"