It seems that, by losing their HRH style, the children are officially no longer "prince/princess of Sweden" and will only retain the prefix of prince/princess before their names as a matter of courtesy, like the King's sisters who married unequally. CP's and Madeleine's grandchildren on the other hand will be untitled.
There is still a legal confusion, however, about the line od succession, which I hope the Court will clarify. The Act of Succession says that "[FONT=Arial,Helvetica]The right of succession to the throne of Sweden is vested in the male and female descendants of King Carl XVI Gustaf," CP's and Madeleine's grandchildren will stiil be "male and female descendants of King Carl XVI Gustaf" and, accordingly, my understanding is that they will still be in the line of succession even if they are untitled. Removing their succession rights would require an amendment to the Act of Succession, which could only be enacted in accordance with the special procedure laid out in the Instrument of Government.
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[FONT=Arial,Helvetica]The Act of Sucession, however, lists several situations that cause someone in the line of succession to lose his/her succession rights, for example, not professing the Lutheran faith as adopted by the Church of Sweden, marrying without the consent of the Swedish government upon application by the King, or becoming the head of a foreign State without approval of the King and the Parliament of Sweden, The problem is that all the aforementioned conditions apply specifically in the text to "princes and princesses of the Royal House".[/FONT]
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[FONT=Arial,Helvetica]Prior to today's announcement, there was an assumption that "princes and princesses of the Royal House" included in theory all persons in the line of succession , but that does not seem to be the case now as, according to the official statement by the Court, CP's and Madeleine's children are no longer princes/princesses of the Royal House, but remain nonetheless in the line of succession. If we now interpret the Act of Succession literally then, the conclusion is that they are now free to change their religious denomination, marry without consent, or become another country's sovereign without consent and still retain their right of succession to the Swedish throne, whereas, for Estelle and Oscar, all the former restrictions still apply.
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[FONT=Arial,Helvetica]So, let's assume an unlikely scenario where Estelle and Oscar for some reason are disqualified from the succession together with their descendants, for example for marrying without consent, and Alexander is now direct in line to the throne after his father, but Alexander himself also married without consent or converted to Roman Catholicism. Could the restrictions in the Act of Succession apply retroactively to him then (since they didn't apply before when he was no longer a prince of the Royal House) ?
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[FONT=Arial,Helvetica]As I said, it looks very confusing to me because titles have been separated from succession rights (which is OK), but certain important rules affecting the succession seem to apply to titled persons only.
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