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In OTL Emperor Basil II refused to get married because he didnt wanted to associate anyone with his throne especially the nobles (while other sources mention that he didnt marry because of the emotional trauma suffered by his mother's intrigues)and spent most of his time with his soldiers... thus leaving the throne to his brother Constantine VIII and his daughters (to who also was reluctant to let them get married and have heirs) causing the end of the Macedonian dynasty...
WI Basil II had a (bastard) son? Basil II despite his hatred towards marriage he was quite a "ladies man" so he could have sired a son...
Could he make him his heir? Basil II had the complete loyalty of the army so he could rely on them to proclaim his son as Emperor... The only problem in that would be the nobles and the Church? How would they react to Basil's bastard as Emperor? Is such a case possible?