Tosfos (Eiruvin 80b) asks why is it that kitusei michtas shiura disqualifies a korah made from an asheira but does not disqualify a lechi made from an asheira. Tosfos answers that a korah requires a shiur of at least a tefach; a lechi has some shiur of height and width, but it is an insignificant amount (the width can be a mashehu). Tosfos then quotes R' Avraham as answering that if you took the lechi and broke it into little, tiny pieces, so long as you affix those little pieces together on a wall, it is a valid lechi. The same cannot be said of a korah, as the little pieces would collapse.
It seems that the two answers of Tosfos differ in their conceptual understanding of kitusei michtas shiura. According to the first answer, kitusei michtas *shiura* means that there is not enough "stuff" there, there is a lacking in the shiur required. A lulav made from an asheirah, for example, is pasul because it does not meet the requirement of being 4 tefachim tall. According to the second answer, there is sufficient "stuff" present -- what is lacking is tziruf, something to hold the parts together. It is as if that lulav, that korah, etc. are broken into little bits. That has no effect on the kashrus of a lechi.
The Ran asks why is it that a get can be written on issurei hana'ah -- why don't we say kitusei michtas shiura? Ran answers that there is no shiur for a get. It seems that the Ran held like the first model of kitusei michtas shiura, that it is a lack in shiur. According to the second model, even if get does not need a shiur, it would not do much good if it is ripped into little shreds. (See the Steipler in Sukkah who tries to get these two models to mesh together.)
Achronim discuss whether kitusei michtas shiura applies to ner Chanukah. The Aruch haShulchan quotes the second answer of Tosfos in Eiruvin and writes that even if the oil is broken into little drops, who cares? So long as it burns for the required time, you should be yotzei. Perhaps one could counter argue that according to the Ran kitusei michtas means it is as if there is a lack in the shiur of oil required to be lit.
Alternately, one might argue that there is in fact no shiur for the amount of oil that must be lit. This is Chanukah after all! Assuming the one jug the Chashmonaim found was broken into 8 parts, each day they lit with less than the shiur and nonetheless it burned for sufficient time. Ad she'tichleh regel min ha'shuk has nothing to do with how much "stuff"/oil there has to be -- it just tells us how long the menorah has to remain lit.