A Mishna in Chagigah 20b explains that sanctified items placed in the same sanctified vessel are considered combined for purposes of impurity; for example, if a tvul yom touched one, everything else in the vessel would become impure. However, this is only if they are all touching. The sons of Rabbi Chiya asked Rav Kahana if that would hold true even if they weren't touching. Rav Kahana derived from the word "tzeiruf" used in the Mishna there that they would combine. They ask two more related questions and Rav Kahana answers them.

Then, Rav Kahana asks them a question about whether combining two items in a bowl, when not touching, would be valid for taking a kemitza (if the dough of the mincha was split into two parts). They attempted to make a comparison between the case in question and the case in our Mishna regarding the two minchas that got mixed together. However, Rava rejects the comparison as it is likely they were touching.

Rabbi Yirmia asks a follow-up question about items being connected regarding impurity—in a case where the item is attached through water (in a pipe) to something outside of the vessel. Would the impurity extend to there as well? Or what if the outside piece became impure, would it extend to the other piece in the bowl as well?

If a mincha offering was divided and one part became impure and was then added to a bowl with its other half, if a tvul yom then comes and touches the impure half while it is in the bowl with the other, is the other piece impure as well? This is in essence asking whether once something is impure, can impurity be added again? Rava asked this question and Abaye tried to answer it from a Mishna in Keilim 27:9, explaining that there is no such concept that once something is impure it cannot become impure again, but Rava rejects his proof as the cases aren't comparable. The Gemara further tries to prove Abaye's point from the continuation of that Mishna, but that is rejected as well.

Rava and Abaye disagree about a case where there are three pieces—two from the original, one of which was lost temporarily, and a third that came to replace the lost half. What is the relationship between the three for laws of impurity and laws of kemitza?