I'm not sure all modern European states ever had a monarch to begin with. Take Finland for example, would the Swedish king be considered the traditional ruler, as Finland was part of the Swedish kingdom for so long? But then, the current monarchs dynasty never actually ruled Finland, as they've only had the throne since after Finland was no longer under Swedish rule.

Basically what I'm saying is, depending on the rules of the game, this could become quite complicated and ambiguous.

Bayezid Osman is the current head of House of Osman so he would be Sultan of Ottoman Empire. Georg Friedrich Ferdinand, Prince of Prussia is current head of House of Hohenzollern and would be monarch of German Empire and Kingdom of Prussia. Similarly Line of succession to former thrones are still informally kept for other former Imperial houses as well if members of those houses are still alive.

Ireland: Desmond O'Conor Don, descendant of the younger brother of the last High King of Ireland, Ruaidrí Ua Conchobair.

Scotland (if assuming Stuart pretenders): Franz Bonaventura Adalbert Maria Herzog von Bayer (great grandson of the last King of Bavaria, Ludwig III)

Germany: Georg Friedrich Ferdinand Prinz von Preußen (great-great-grandson of Wilhelm II).

Finland (if using the senior Vasa hier): Maria Vladimirovna Romanov.

Russia (and Byelorussia, Ukraine, Estonia, Latvia, Lithuania and the various formed Soviet states): Nikolai Kirillovich Romanov. This one is tough - House rules on marriage and conduct might very well disqualify several candidates. Maria Vladimirovna Romanov has a greater claim, but Russia had salic law, meaning females could not inherit.

Poland: Ladislas Poniatowski might be a candiate (currently a French politician) as House Poniatowski provided the last native elected King of Poland-Lithuania in Stanislaw Poniatowski.

France (if legitimist): Luis Alfonso Jaime Marcelino Manuel Víctor María de Borbón y Martínez-Bordiú or (if orleanist): Henri Philippe Pierre Marie d'Orléans.

Portugal: Dom Duarte Pio, Prince Royal of Portugal, Duke of Braganza.

Italy: Emanuele Filiberto di Savoia, or if the claim of an undynastic marriage holds, Amedeo Umberto Costantino Giorgio Paolo Elena Maria Fiorenzo Zvonimir di Savoia-Aosta.

Ottoman Empire: Prince Şehzade Dündar Aliosman Efendi.

Greece: former King Konstantínos II

Serbia (and all of Yugoslavia, should it exist): Alexander II Karađorđević.

Austria (and Croatia, Czechia, Bosnia, Bohemia, Hungary, Slovakia and Transylvania): Karl von Habsburg.

Bulgaria: Simeon Borisov Saxe-Coburg-Gotha (briefly King as Simeon II).

Romania: Mihai I (who was King until 1947).

Iceland: Queen Margerete of Denmark.

Switzerland: Well, this one is tough. Switzerland was de Jure part of the Holy Roman Empire, so Karl von Habsburg would be a candidate.

Who should it be and who would it be is a difficult enough question even for countries that still have monarchies. In England, who's to say that the Jacobite pretender shouldn't be king other than Parliament and force of arms? If you were to disregard the parliaments of other countries, why not here? It's all a sticky mess that I gladly leave to armchair heralds.

Not Europe, but our royal family is directly related to some important European families.

The right to the throne of an eventually resurgent Empire of Brazil is disputed by two branches of the House of Bragança: the Petrópolis branch and the Vassouras branch. Both branches descend from princess Isabel de Orleans e Bragança, oldest daughter of Emperor Pedro II of Brazil.

The current head of the Petrópolis branch is prince Pedro Carlos de Orleans e Bragança, and the head of the Vassouras branch is prince Luiz de Orleans e Bragança.

The Petrópolis branch have the stronger genealogical claim, but their ancestor Pedro de Alcântara renounced his rights in 1908, so the Vassouras branch have better legitimacy.

In practice the probability of that ever happening is so small that it's almost irrelevant to keep track who would have any claim.

Edit: Removed previous edit for lack of supporting information. I don't know if the Saxe-Coburgo Bragança branch can have any claim.

Simeon II would be our Tsar (Bulgaria)

Interestingly he was Tsar for 3 years (1943-1946 under regency) before the communists abolished the monarchy. Then after the fall of Zhivkov he came back in the early 00s and became our Prime-Minister (2001-2005).

If monarchy wasn't abolished when he dies his grandchild Boris would've taken the throne as Boris IV.

Sorry if I break the rules I think that's what OP wanted to know.

I guess the answers for Sweden, Denmark, Norway, Britain, Spain, et al. would be rather uncomplicated, as the countries already are monarchies.

Does anyone have any thoughts on Ireland? The situation is pretty muddy from the various influxes of settlers and occupiers, I'd assume.

Sorry, but your submission has been removed because we don't allow hypothetical questions. If possible, please feel free to rephrase the question so that it does not call for such speculation, and resubmit Otherwise, this sort of thing is better suited for /r/HistoryWhatIf.