In general women take on their husband's title, Duchess of Cambridge/Sussex, Princess Michael of Kent. In the past untitled men who married in would be given/offered a title, usually an earldom. Princess Margaret's husband was untitled and offered the earldom of Snowdon after their marriage. Anne's first husband was also offered an earldom which he declined. Had he accepted Peter and Zara would have been styled as the children of an earl. That was probably the last time something like that will be offered. Jack and Edo will remain without titles and as titles are passed down in the male line their children will remain untitled. As for Edward and Sophie's children, assuming they remain styled as children of an Earl, and in the future Duke... Louise's children will have no titles unless she marries someone titled, James' children will be styled as the children of an Earl/Duke depending on his title at the time. When he inherits the dukedom of Edinburgh after Edward it will technically still be a royal dukedom as he is the grandson of a monarch but should he have a son when that son inherits it will cease to be a royal dukedom. It will be interesting to see what happens with the Cambridge kids..... based on current traditions George will likely be Prince of Wales by the time he marries and Louis would be given a dukedom upon marriage. Charlotte would be expected to become Princess Royal but the optics of the younger son getting a dukedom and not his older sister will probably look very bad by then.