what will be the status of owned property in Israel when Moshiach comes.
Will a person's apartment remain his? or perhaps the land will be redivided.
First, it must be remarked that a Jew can own a plot of land in the Galil but actually rents a house and lives in Netanya. Ownership does not oblige you to live on your property. (That is how Israel "owns" land East of Jordan and in South Lebanon because they are the inheritance of Israel even though no Jew lives there or claims his property - yet...)
Two, in order to have property according to the division of the Land among the tribes, all Jews must be present to claim their property and each one must know to which tribe he belongs. This will be the task of the Minister of Interior of King Meshiah, as Rambam writes in Laws of Kings and Wars Ch. XII: בימי המלך המשיח, כשתתיישב מלכותו ויתקבצו אליו כל ישראל יתייחסו כולם על פיו ברוח הקודש שתנוח עליו... הנה למדת שברוח הקודש מתייחסין המוחזקין ומודיעין המיוחס. ואינו מיחס ישראל אלא לשבטיהם
Three, Yehoshua divided the Land by drawing lots although each tribe knew which part of the Land is his. By inference, we are entitled to imagine that when Meshiach will relate each Jew to his tribe, we will find out that he already lives on his part of the Land... in the meantime, the task of the State of Israel is to prepare the way for Meshiah. בקרוב בימינו.
In the Navi Yechezkel (ch. 48, vv. 23-28), the aportionment of land is discussed. At a very basic level, it seems that the land will be redivided, and people have to determine which tribe they're from. Owning an apartment in Eretz Yisrael, while virtuous, doesn't necessarily mean you actually own physical land. The owner of the apartment block may own the land, but according to many statutues in Eretz Yisrael, the land itself might be owned by the government, and it leased to the owners of the block. In this sense, you're a 'renter'. This government really owns the land, so the apartment 'owner' simply owns the rights to use that space as the government allows. When Moshiach comes this will become irrelevant, and I assume all Jews will be given their allotted portion, depending on the tribe they belong. So you might own a 2-bedroom in Jerusalem, but the reality is that Hashem wants you to have a plot of land in Netanya. You might own nothing, and you live in Brooklyn as a renter, and Hashem has a plot in Jerusalem set aside for your family.
As regards actually owned property, that you have the title deeds for, or you have a chazaka on the land (3 years), assumes that you have a valid claim of ownership (Rashi on Bava Basra, Chezkas Habatim, 3rd Perek). However, it could very well be that Moshiach will simply aportion land up differently based on Navua (It is an interesting question: Reuven has a chazaka and Shimon has a message from the urim v'tumim that it belongs to Shimon. However, if everyone is receiving a new portion then it seems that any prior ownership will become irrelevant (that is the implication of Yechezkel).
Great question. This is a multi faceted question, the crux of it is, are current land deeds valid in a torah-run state, i.e. after mashiach comes. The simplest answer is no. The torah (Deut. 26) clearly outlines how the Land must be divided (by tribes and families), and the current land deeds are not sales from original owners but rather legal deeds issued by the State of Israel, which has no power that I know of, to override a biblical command. The challenge, however, is how to go about splitting up the land. The basic idea is clear in the Torah and the Talmud - meaning the general outline of each tribe. Elijah and Mashiach should be capable of figuring out the rest... Current land owners in Israel, though, should be able to get repaid for any investment they put in to improve their property (for the time being they do have ownership of the property). One more point I would make, is to speculate that this will not be an over - night process; even in Yehoshua's time (the first time around) it took 7 years to work it all out. Also many deals will probably be struck to maintain the comfort of the most people possible. (expect to hear a lot of "tikun haolam".) May hashem help this important question become relevant in no time.