Do I need to be concerned if I have a significant other move in with me? I own my own home outright ...no mortgage.... And am a widow. Will he have

Well, if your concern is whether having him move in will give him ownership rights in the property, the answer is no (assuming you don’t sign anything over to him).  However, once it becomes his primary residence, he doesn’t have rights to remain in the property.  That is, if things go south, you can’t just kick him out and change the locks.  Instead, you’ll probably have to file an unlawful detainer or ejectment.  Nevertheless, that’s really more of headache to be aware of rather than something to be concerned about with regard to losing any of your rights as the owner of the property.  Of course, that answer changes if you two get married or you start signing things over, but just having him move in doesn’t diminish your ownership.