The phrase "hadst law on" can be interpreted as having control or dominance over something. Synonyms for this phrase include "exercised authority," "enforced regulations," "presided over," "ruled," and "governed." Other possible alternatives may include "held sway," "dominated," or "dictated." Context and usage will determine which synonym is most appropriate. For instance, in legal or governmental situations, "enforced regulations" or "governed" may be more fitting. In contrast, in personal relationships or social contexts, "held sway" or "dominated" may be more relevant. Ultimately, the selection of a synonym will depend on the intended meaning and the nuances of the situation.