These junior lines become more frequent the further back you go.
For instance, Elizabeth's mother, Elizabeth Bowes-Lyon, brings in a closer descent to the Seymour monarchs, Edward VI and Lady Jane Grey. Prince William, Duke of Cambridge, if he becomes king, will add lines to Charles II and James II, from whose illegitimate children he is descended through his mother Diana, Princess of Wales.
All 4 lines start with Henry IV's younger son Humphrey of Gloucester and granddaughter Antigone of Gloucester, and all 4 of them end with Elizabeth II's mother Elizabeth Bowes-Lyon, grandmother Nina Cavendish-Bentinck, and great-grandfather Charles Cavendish-Bentinck.
There are 4 lines of descent from Henry IV to Elizabeth II.
The conflict ended when Stephen recognized Matilda's son Henry as his successor.
Matilda asserted her claim, leading to a protracted war (the Anarchy).
He became king by overthrowing his cousin, Richard II in 1399.
*NB Second line of descent from Llywelyn the Great through his natural daughter, Gwladus Ddu through her son, Roger de Mortimer.
There are many other more junior lines of descent of the family, but the crown, in theory at least, only descends through the most senior line (a major exception being the exclusion of the genealogically senior Jacobite succession by the Act of Settlement 1701).
Owing to extinct lines, large parts of entire royal houses (Lancaster, Tudor, Stuart) are bypassed in the current most senior line.
Christiane Emilie von Schwarzburg-Sondershausen 19.
Dorothea of Brandenburg, Duchess of Mecklenburg 13.