As writers we are always looking for the romantic lost heir or the kindly noble who adopts a child to inherit his title, but rules of inheritance both of titles and entails are quite strict.
Titles pass through the eldest son and if the family is unlucky and begets only daughters, the title will return to the crown, known as going into abeyance. As always there are exception to the rule, you only have to look at the Churchills to find one.
There was no such thing as adoption during the regency. A child could become a ward of court, or of a relative, but only the male of the blood line could inherit a man's title and entailed land. Money and items not deemed part of the entail could be left to anyone of course.
This is true for illegitimate children also. If the mother was not married to the father at the time of the birth, then the child cannot inherit. The obverse was true. No matter who sired the child, if the man was married to the woman at the time of the birth, and if it was a son, then the child would inherit. This is of course why men could be cavalier about their affairs, and their wives were held to a much higher standard of behavior at least until they had their heir and their spare.
There are of course some interesting examples of this latter scenario. Jane Elizabeth Harley, Countess of Oxford, pictured here by Hoppner, provided her husband five children who were mostly half-siblings, and resentfully acknowledged by the scandalous lady's husband. Byron was one of her lovers for a brief time, though there is no indication that he sired any of her children.
The case of the Earl of Berkley is also fascinating. On his death, his former mistress who gave him four sons, who later married him and gave him another son, tried to have her older sons made heir by saying she and the earl had entered into a "secret" marriage. The Prince of Wales had the whole affair investigated and in the end it was the youngest son who inherited. A bit sad for the older boys, I think. And rather ironic when you remember Prinny's own secret marriage.
If they had been in Scotland it might have been another story for in that jurisdiction, provided the couple were not previously married to others when the children were born, and subsequently married, the children could be claimed legitimate.
Until next time, Happy Rambles.