Heirs and Inheritance
Male primogeniture is the rule. That is, the eldest son inherits everything (including debts) unless provision is otherwise made for younger sons.
The eldest son gets the title, even if the oldest child is a girl.
In very rare occasions, a title and lands may pass in the female line. For example, a secondary title to the Manners earls of Rutland is the barony of DeRoos (one of the oldest in the kingdom), in which the title passes simply to the eldest child, regardless of gender. Although her younger cousin (as eldest male) became the earl, Lady Elizabeth Manners (as eldest child) became the Baroness de Roos in her own right.
A will takes into account provision for a daughter's dowry, which the heir is bound to honour.
When a peer dies leaving a minor heir, that child becomes a ward of the Crown. That is, the Crown takes responsibility for the education and marriage of the heir until he comes of age at 21.
The costs of this responsibility are paid out of the third of the deceased peer's estate that is dedicated to the upbringing of the heir as a Crown ward. The office of Master of the Court of Wards (held for a long time by Burghley) is a very lucrative one. (Other orphans are managed by the Court of Orphans.)
Often some other gentleman applies to buy the marriage rights of such a ward, and takes the responsibility (and the income) for the child's upbringing. Usually this means taking the child into his own home, administering their estate, and profiting from the result.
Sometimes the heir's mother is awarded these rights herself.
When the heir comes of age, he must sue the Crown for the return of his livery and maintenance.
An heiress is a daughter with no brothers and no clear male heirs. If there are several girls, they will be co-heiresses. (This can get complex. Consult a herald.)
When there are only daughters and no clear male heir, the girls inherit the property and the title goes into abeyance until or unless a male heir can be proved.
A bastard is a child born out of wedlock. By law, any child born in wedlock is legitimate, with some exceptions. If you are living openly with another man and having his children, your lawful husband doesn't have to accept them as his own.
A bastard is also called a natural child. Illegitimate children can be legitimated only by royal decree.
Fox-Davies: A Complete Guide to Heraldry
26 March 2000 pkm