From Wikipedia: Before 1953, various descendants of King Christian IX had succession rights in Denmark. The new Act of Succession terminated those rights but left the individuals involved in possession of their titles. This created a class of people with royal titles but no rights to the throne. As a distinction, those entitled to inherit the throne are called "Prins til Danmark" (Prince to Denmark, although this distinction is not made in English) while those without succession rights are referred to as "Prins af Danmark" (Prince of Denmark).
I took the liberty to bold and italicize what is exactly the crux of the issue, i.e. personages who were
born prior to 1953 and thus, when the Act of Succession was passed (in 1953),
were in possession of title of Prins/esse til Danmark. As of 1953, such personages, i.e. the descendants of King Christian IX but who were not issue of King Christian X and Queen Alexandrine, as the then Diadoch Constantine of Greece, Princesses Sofia and Yriny of Greece and Princes Peter and Michael of Greece,
ceased to be constitutional Princes/ses of Denmark (ie,
til=to) and became automatically
courtesy* Princes/ses of Denmark (ie
, af=of).
To make the point crystal-clear, the
til and
af Danmark, as used in Denmark in conjunction with the prince/ss title, correspond to what in the English language are
periphrastically referred to as prince/ss in his own right (a constitutional prince/ss - a
dynast) and prince/ss by marriage/association (courtesy prince/ss - a
non-dynast), respectively.
By definition, however, a holder of a courtesy title has
no own dynastic right to transfer her/his title to one's issue. Said differently, the children of King Constantine were not born princes/ses til Danmark since, at their birth, both their father had ceased to be a Danish dynast and the 1953 Succession Act precluded that altogether. Lastly, I am not aware of princes/ses af Danmark born to princes/ses who were mere princes/ses af Danmark.
Therefore, unless HM The Queen of Denmark decides, through
letters patent or some other Danish royal prerogative provided for by the Danish Constitution, to confer officially courtesy titles to them, the children of King Constantine are not princes/ses either til or af Danmark. Should there be a way for HM The Queen to do so, it would complicate matters for, in such case, the children of Princess Benedikte - who after all remains a princess til Danmark, could and would also have similar expectations, etc etc.
* Here the term
courtesy prince is used (see unabridged Merriam-Webster) to imply presence of official right but absence of legal meaning/significance. For example, Prince Henrik af Danmark and Princess Mary af Danmark are not dynasts -
they may not issue princes/ses in their own right.
By the way, a
courtesy title is inferior to
ad personam titles. For example, the Infanta Elena of Spain is the ad personam Duchess of Lugo. Her title is for her only and cannot be inherited, but (she) shall remain so for life, whether she divorces or remarries. On the other hand, Princess Alexandra of Denmark lost her courtesy title of princess the very moment she remarried. So a courtesy title, apart from legally meaningless may also be conditional.