As is so often the case, with the passing of the Founder, religious or spiritual organisation tends to fragment; the one strong and inspiring personality being replaced by a number of lesser, well-meaning but still perhaps egoistic ones. The Theosophical Society after Blavatsky was no exception. [Note: the following historical material is taken mainly from selected articles in Richard Cavendish, Ed, Encyclopedia of the Unexplained (Routledge & Kegan Paul, 1974)]
Blavatsky immediate successor as head of the Society was Annie Besant (1847-1933), a British social reformer, feminist, and atheist. An ardent Anglo-Catholic as a girl, she later adopted atheism and became a leading figure in the National Secular Society, publishing The Gospel of Atheism in 1877. She was unsucessfully prosecuting for selling "obscene literature" - a book on birth control. In 1889 she abandoned atheism and joined the Theosophical Society, and swiftly rose rose to high office as an enthusiastic advocate both of Blavatsky's teachings and of social reform, and become head after the death of Blavatsky in 1891.
Originally, Mrs Besant was on good terms with both Judge and Olcott, sharing the esoteric interests of the former (becoming with him joint head of the Esoteric Section), and the desire for social reform of the latter. But a year after Blavatsky's death, both Besant and Judge claimed to have received letters from the Masters appointing them each head of the Society. A few years later, matters came to a head, and in 1895 Judge succeeded with the majority of American Theosophists from Besant and Olcott's Adyar group. He also claimed that he was Koot Hoomi (or an incarnation thereof), the Occult Master who inspired Blavatsky. Judge himself died a year later, and was eventually replaced by Katherine Tingley (1847-1929), the "Purple Mother", a spirit medium with an interest in welfare work, who founded her centre at Point Loma in California, a sort of American Adyar. After her death Mrs Tingley was suceeded by Gottfried de Purucker, a capable but voluminous author of works of Blavatskyian Theosophy. Most of his material is now avaliable on-line.
Meanwhile, with Olcott's death in 1907, Mrs Besant - who despite her passion for esotericism seemed to have had no original intuition or clairvoyance of her own - came under the influence of Charles Webster Leadbeater (d.1934), originally an Anglican clergyman with an interest in Spiritualism and young boys, who joined Blavatsky's Theosophical Society (although he made grand claims regarding his status there, he was never admitted to the Esoteric Section, and the Old Lady when in a less than charitable mood used to refer to him as "W. C. Leadbeater" [Tillet, p.54]).
Whatever Leadbeater's vices, he was a capable clairvoyant, and either alone or in conjunction with Mrs Besant the author of a number of excellent books on the nature of psychic and occult phenomena. Eventually it was Leadbeater and Besant's writings, rather than Blavatsky's, that were to form the basis for Theosophical metaphysics.
The reason for this is not hard to see. Blavatsky's writings sufferred from a terribly difficult and unsystemmatic style. A good attempt to make her teachings comprehensable was made by A. P. Sinnet, the edtor of an influential Anglo-Indian paper, The Pioneer, who's two books Esoteric Buddhism and The Occult World introduced Theosophy to Europe in the 1870's. But it was really Leadbeater and Besant's many books that made the general Theosophical cosmology accessable; although their writings have been disparagingly referred to by Blavatsky purists and Point Loma and other Non-Adyar factions of the Soceity as "Neo-theosophy", as distinct Blavatsky's own teachings ("Theosophy").