You may certainly word this otherwise, but in this context "unipersonal" describes an entity that has a single shareholder (in the case of "sociedades anónimas") or a single member (in the case of "sociedades limitadas" in which "socios" can generally not be referred to as shareholders).

"Unipersonalidad" can be "originaria" (the entity is initially incorporated as a single-shareholder/member entity), or this circumstance is devenida" or "sobrevenida" (the entity is subsequently converted into a single-shareholder/member entity when for some reason all shares or "participations" are subsequently owned by a single shareholder/member.




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Note added at 34 mins (2020-09-10 19:46:17 GMT)
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To add a comment to Helena's references: I think it's important not to confuse "sole proprietorship" (which describes an individual in business for himself; in Spain called "empresario/comerciante individual") with "sociedad unipersonal" (which in Spain denotes an incorporated entity that has a single shareholder/member).

To mention only one (but quite significant) difference, a "sole proprietor" (called "sole trader" in the UK) has unlimited personal liability for all of his business debts. A shareholder is only liable for the amount of his investment in the business, i.e., the price paid for his shares.