The Mishna says that if a ba'al habayis has a tefisas yad in the homes that he lends or rents out, they don't need an eiruv to join them together. The gemara tells a story of a wealthy person who lent out many homes in his chatzer but retained a place for keilim in each one thereby circumventing the need for an eiruv.
Regarding the types of items that qualify as a tefisas yad, the gemara says a rule that anything which isn't muktzah and may be moved on shabbos doesn't qualify as tefisas yad, but things that are muktzah do qualify. Rashi explains why non-muktah items aren't considered a tefisas yad - דאי בעי שקיל ושדי ליה לבראי.
It isn't clear from Rashi whether he means that we are concerned that the owner will remove the items, or whether the renter will throw out the items. In other words, are we speaking about a case where the owner has legal rights to leave the items in the renters property, just that we are still afraid that he may need his items and remove them, so we insist that they be muktzah; or does the muktzah item allow us to consider the owner to have a tefisas yad even if he has no rights to actually leave his item in the renters home?
The Mishna Berura (370:11) says that the owner must legally retain rights to leave items at least in some small corner or section of the renters home. The Sha'ar Hatziyun (8) cites the Mordechai and Ritva as the source. The Bach understood from Rashi that even if the renter has the right to throw out the item, it qualifies as tefisas yad since the item cannot practically be moved on shabbos due to its muktzah status. The Sha'ar Hatziyun disagrees with the Bach and says that Rashi means that the item must be muktzah to prevent the owner from removing the item, but in addition the owner must have legal rights to actually store the item there.
Based on this halacha we generally assume that in an apartment building or complex in which the apartments are rented out, there is no need for an eiruv since the owner has a tefisas yad by the refrigerator or oven that he has in the apartment. In light of the halacha above, it must be a situation in which the renter doesn't have the right to discard the refrigerator and oven, and instead purchase one of his own. If the owner for example tells the renter that the oven is there for his convenience, but it is an old oven so if you want you can throw it out and purchase your own, it would not qualify as a tefisas yad.