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To be specific, to get to the present Royal family from Edward III, the Royal line had to pass through female lines no less than 7 times. Most times the surname changed, though sometimes the wife's surname was kept.
This is a lot of female lines and name changes. For comparison, my wife's descent from Edward III involves only 5 passes through female lines. And if I prove the Blennerhassett link then I myself have a descent from Edward III with 7 passes through female lines. In the Neville family are people whose descent from Edward III involves only 1 pass through a female line. And in the Somerset family are people with a direct male-line descent from Edward III and the medieval House of Plantagenet (no passes at all through female lines).
In short, the current Royal line is the product of a series of political decisions rather than being ordained naturally by descent. Nowhere is this illustrated more clearly than in the extraordinary succession of the House of Hanover.