I
The Gemorah (Kerisus 9a) tells us that all of the laws of geirus (conversion) were established by the chachomim based on the Torah's description of ma'amad Har Sinai, which was the national geirus of the entire Jewish people. The first, and absolutely indispensable, requirement is kabolas ol mitzvos, i.e. the convert must commit himself to observe all mitzvos, just as on the occasion of ma'amad Har Sinai the entire Jewish people declared, "na'aseh v'nishmah". The second requirement for conversion is derived from the fact that prior to bringing the korban Pesach in Mitzrayim, all of the men had to have a bris milah. The Gemorah understands that this is not only because an arel may not eat korban Pesach, but was also the first step in geirus, as is required for converts in all the future generations. Immersion in a mikvah is also a required part of conversion and is learned from all of the Jewish people having to go to the mikvah immediately before ma'amad Har Sinai. If we would just read the pessukim in the chumash we would get the mistaken impression that only married couples had to go to mikvah. However, the Gemorah points out that if one reads in between the lines, one understands that even the single people had to undergo tevilah as well. And finally, towards the end of parshas Mishpatim, the Torah tells us that special korbanos were offered at Har Sinai, which the Gemorah understands to indicate that a korban is required of every Ger throughout all generations.
At first glance, one might think that the requirement for a ger to bring a korban would make conversion impossible today. The Gemorah points out, however, that the Chumash indicates that converts can be accepted in every generation even though the Torah speaks of a possibility of a generation where there is no Beis Hamikdash. The Gemorah explains that geirus is completed even before the korban ha'ger is offered, but the ger is not permitted to eat other korbanos until he brings his korban ha'ger. The Gemorah says that anyone who converts today and will still be alive when the third Beis Hamikdash will be built will be required to bring his korboan ha'ger at that time.
II
In addition to kabolas ol mitzvos, tevilah, and korban, the Torah (24:7) describes another event which took place during ma'amad Har Sinai, namely that they read from the "sefer ha'bris." Rashi (ibid) quotes from the Tanoim that the sefer ha'bris consisted of all of sefer Bereishis and Shemos up until ma'amad Har Sinai. If all the laws of geirus were established based on what took place at Har Sinai, why don't we have the practice to read from the sefer Torah when someone converts?
On the occasion of ma'amad Har Sinai the Torah was accepted by the entire tzibbur and the bris was made with the tzibbur as a whole, not with individual Jews. Perhaps the requirement of reading from the sefer ha'bris only applies when there is a kabbolas ha'Torah by the entire tzibbur because the bris was made with the entire tzibbur as well.
The Gemorah (Shabbos 88a) understood from the phrase in Megilas Esther (9:27, "kiymu v'kiblu") that on the occasion of the neis Purim there was another kabbolas haTorah by the entire tzibbur. The Gemorah also understands from another phrase in Megilas Esther (9:30, "divrei shalom ve'emes") that the megilah is compared to "amito shel Torah", which Rashi understands to refer the sefer Torah[1]. [On the occasion of Ma'amad Har Sinai, the sefer ha'bris only consisted of everything in Bereishis and Shemos up until Sinai. Once Hashem dictated to Moshe Rabbeinu how to assemble the chamisha chumshei Torah at the end of forty years of traveling in the desert, the entire sefer Torah had the status of a sefer ha'bris.] The national kabbolas ha'Torah on the occasion of neis Purim created the requirement to read from another sefer ha'bris, namely Megilas Esther.
The sefer Torah and Megilas Esther share in common a din based on the fact that they both have a special status of sefer ha'bris. The Rambam writes that if you write Torah, Nevi'im, and Kesuvim in one continuous klaf, you can't lein kri'as ha'Torah from it. While it is true that the Nevi'im and Kesuvim have the status of Torah b'ksav, they do not have the status of sefer ha'bris. The Rambam uses the expression, "yeser ko'notal" (which appears in the Gemorah in a totally different context) to say that if you add something to the Torah which is not sefer ha'bris, it pulls down the status of the sefer Torah. If we would lein from a klaf which has only one parsha in it, that would be considered kri'ah shelo mitoch ha'ksav. Alternatively, if we would lein from a klaf which contained an entire chumash, e.g. sefer Shemos, the kri'ah of would be considered mitoch ha'ksav because we have a sefer sholeim, but it is not considered a kri'ah from a sefer ha'bris. Because the bris was made with the entire tzibbur, the Gemorah (Gittin) says it is a violation of kavod ha'tzibbur not to read the parshas ha'shavua from a sefer ha'bris. The Rambam adds that if you have the entire Tanach together in one klaf, since the other nineteen seforim are not sifrei ha'bris, that copy of the Chamisha Chumshei Torah loses its status of sefer ha'bris and can't be used for kriyas ha'Torah.
The Gemorah says that this same din of kavod ha'tzibbur applies to kri'as ha'Megilah. If one has all of the five megilos together in one klaf, because the other four megilos are not considered sifrei bris they lower the status of this copy of Megilas Esther. If one were to lein the megillah without a minyan, reading from such a klaf would be fine, since it will be mitoch ha'ksav and from a sefer sholeim. However, it would not be acceptable for reading the megillah in a minyan. Because the bris was entered into with the tzibbur, the tzibbur must hear kri'as ha'megillah from a text that has the status of sefer ha'bris, but there is no such requirement for yechidim.
[1] Tosfos disagrees with Rashi regarding the meaning of the phrase "amitoh shel Torah". However, in the sefer Kedushas Levi, the Barditchiver points out that the Talmud Yerushalmi seems to have understood like Rashi and not like Tosfos.