1. Generally known and spoken of, usually unfavorably.
2. (Of the possession of property) so conspicuous as to impute notice to the true owner. — aka (in sense 2) open and notorious. 
1. Well known; a matter of public knowledge. 
notorious possession – The possession of real property in a clearly defined and open manner. 25 Am J2d Eject § 43.
open and notorious –
1. A phrase applied to a number of concepts and terms in the law, which refers to acts that are deliberately not conealed and that are conspicuous and a matter of public knowledge. Thus, for EXAMPLE, open and notorious possession means conduct sufficinet to put a person of ordinary prudence on notice that hi land is the subject of an adverse user or adverse possession; and open and notorious adultery refers to a man and woman openly engaged in adultery or fornication, or openly living together outside marriage. 
1. Acts upon the land of another which are not in secret but of such a character as to be well calculated to notify the owner of the use made by such acts. 56 Am J1st Wat § 326.
open and notorious possession – Possession evidenced by such a ts and conduct as are sufficient to put a man of ordinary prudence on notice of the fact that the land in question is held by the claimant hs his own. 3 Am J2d Adv P § 47.
Possession of such openness as that the owner’s knowledge of it and of the extent fo it may be presumed. Watrous v Morrison, 33 Fla 261, 278.