In the sefer Ba'er Tziyon [עמוד ו] he writes as follows: וי"ל דיסוד דין חלוקה אליבא דרש"י אינו מכח מוחזקות אלא כל דאוחזין בטלית איכא ספק ודררא לפנינו וחולקין מכח הספק ולא המוחזקות גורם את החלוקה אלא חולקין מכח
ספק וכל דאיכא מוחזקות יש דררא ביניהם שהיא הקובעת את דין החלוקה - According to Rashi the חלוקה is NOT because each side is holding on to the tallis, rather as long as they are both holding on it creates an objective ספק in the mind of the beis din and as a result of this ספק we apply the din חלוקה. This is borne out by Rashi 8a dibbur hamaschil "Mishna Yesiera" - see there.
We must learn this way because as we said in the previous post, each side is מבטל the מוחזקות of the other side so how do we end up giving each side half? It must be that מכח ספק we work out some type of compromise.
This is against Tosfos who understand that there is an אנן סהדי each party owns half.
See the Ba'er Tziyion there, Granat Simman 135, Even Shisiyah Simman 1, Beis Lechem Yehuda page 10, Nesivos Yehoshua page 98, Chiddushim of the Meitchater Illui Simman 95 [he was a Rebbe in Yeshivas Rabbeinu Yitzchak Elchanan and a talmid of Rav Chaim Brisker, who exclaimed (as I heard from the Rebbe Shlita] "A illui ve der Meicheter ich hob nicht gezen in mein leben" - A genius like the Meitchiter I have not seen in my life. Quite a compliment coming from Rav Chaim] and much, much more that the limited scope of this post doesn't encompass.
[Note: I happened to meet a chaver of mine "Reb Moshe Gavriel ben Yehudis" this morning and he told me the same pshat. Reb Moshe Gavriel - maybe you will contribute some of your chiddushim to our blog?? I will speak to the Rebbetzin if necessary to make sure she allows you the time. I am sure she will gladly consent. She wants a talmid chochom as a husband...:-)]