TOSFOS 7b DH de'Is writes that in the same way that the Shtar is invalid without the Toref, it is also invalid without the Tofes, because even if one line of the Tofes is erased the whole document is worthless. Therefore Tosfos writes that the only part of the Shtar which makes a difference, as far as the monetary value that its holder will receive is concerned, is the date.

Therefore if Reuven is holding half of the Toref and Shimon is holding half of the Tofes, it would seem that there is no significance to what each one is holding. However, if the half of the Toref that Reuven was holding included the date (it would seem that this is only meaningful if he was holding the entire date, because there is no value in holding only part of the date) then this would give Reuven an advantage and he would receive the difference in price between a Shtar with a date and a Shtar without a date (from a Shtar with a date one can collect from "Meshubadim" - properties the creditor has a lien on, whilst without a date one can only collect from "Bnei Chorin" - properties which are actually in the debtor's possession, as the Gemara states here). Apart from this difference, the rest of the Shtar would be divided equally. (See SHULCHAN ARUCH 65:15)

D. Bloom

There are different opinions in the Rishonim in the Sugya and according to these opinions the answer to your question will vary.

TOSFOS DH DE-IS concludes that Talmud Yerushalmi cites Rabbi Elazar who maintains that the crucial point is which contestant is holding the part of the Shtar which contains the signature of the witnesses.(Tosfos writes that Yerushalmi disagrees with our Gemara - Bavli).

Therefore according to Yerushalmi if Reuven is holding half of the Toref and Shimon half of the Tofes it all depends if the part of the Tofes that Shimon grabbed included the witnesses. RASHI DH SHTARA writes that the witnesses sign underneath the Tofes. BACH CM 65:18 understands that this means that Rashi explained that the witnesses are considered as part of the Tofes. It follows that if Shimon is holding the place where the witnesses signed, according to Yerushalmi he gets everything.

Even though Tosfos writes that Yerushalmi disagrees with our Gemara, nevertheless according to our Gemara also it can sometimes make a difference who is grabbing the part of the Shtar which contains the signature of the witnesses. This could be the case where "Eidei Mesirah" (witnesses who saw the Shtar being handed over from the debtor to the creditor) are available. in such a case one does not require the "Eidei Chasimah" (the witnesses signed on the Shtar) in order to make the Shtar valid, because the Eidei Masirah alone are sufficient.

Tosfos -just above- stated (see my previous reply) that one does not estimate the value of what each contestant is grabbing if the part being grabbed is essential to make the Shtar valid. However one does estimate the value of what is non-essential. Therefore since Eidei Mesirah are available, the Eidei Chasimah are no longer crucial and one can estimate how much it is worth to be grabbing their signature. The advantage of holding the Eidei Chasimah is that the Eidei Mesirah might emigrate or die and then one could not use the Shtar without the Eidei Chasimah. Therefore if Reuven is holding the part of the Toref which contains the date, and Shimon is holding the part of the Tofes which contains the signatures, they are both holding something meaningful.

Consequently, in such a case, one estimates the relative value of holding the date (see my previous reply that the Gemara says that the advantage of the date is that it enables one to collect from Meshubodim) and of holding the signatures. The one with the more valuable part takes the difference in price between them. The remainder of the Shtar is then divided equally between both contestants. (See TUR CM 65:18 and CHIDUSHEI HAGOHOS #7)

There is another major opinion in the Sugya. This is the Shittah of RIF and RAMBAM who totally omit the Din of Rabbi Elazar about Reuven holding the Toref and Shimon holding the Tofes.

MAGID MISHNEH (Hilchos Malveh Ve-Loveh 14:14) writes that it may be that Rif and Rambam possessed a different text in the Gemara and therefore mentioned nothing about Toref and Tofes. However SHACH CM 65:40 writes that, on the contrary, Rambam had the same text as ours

but learnt the Sugya differently to Rashi's explanation.

Shach explains that according to Rambam (unlike RASHI DH DE-KAYI )Rabbi Yochanan disagrees with Rabbi Elazar. R. Elazar maintains that if Reuven is holding the Toref and Shimon is holding the Tofes each one receives what he is holding. However R. Yochanan disagrees with this. The sentence in the Gemara " even if one is holding the Tofes and one is holding the Toref " is not a question ( unlike Rashi ), but rather a statement - that according to R. Yochanan they split equally even in such a scenario.

Shach explains the reasoning of R. Yochanan. The principle of "each one takes as far as his hand can reach " (see Gemara above 7a) only applies when they are holding a Talis, because the part of the Talis that each one is holding is worth something on it's own. In contrast holding part of a Shtar is worthless because if each one was only holding what was in his hands , i.e. a torn Shtar , this is worth nothing. In addition even a complete Shtar only represents a proof that money is owed but the Shtar itself is not tangible money. Therefore R. Yochanan maintains that one does not take specifically the part of the Shtar that one is holding, but instead one splits it equally.

Therefore if Reuven held half of the Toref and Shimon half of the Tofes, according to Rif and Rambam ,they split the money represented in the Shtar equally because according to this Shittah there is no special advantage of Toref and Tofes over the rest of the Shtar.

KOL TUV

D.Bloom