Rabbi Abba bar Mamla appears to be simply Rabbi Abba [(see there)], except at the end of Chulin where Rabbi Abba answers Rabbi Abba bar Mamla.
In precise Gemaras, Rabbi Abba is not mentioned. [(However, in the Jerusalem Talmud, Chapter 3 of Shevuot, Halacha 2, Rabbi Ba and Rabbi Yirmiyah and Rabbi Bon bar Chiya in the name of Rabbi Abba bar Mamla are mentioned, and perhaps there is a scribal error there, as immediately after this Rabbi Ba is not mentioned)]. Rabbi Zeira said: Throughout the lifetime of Rabbi Abba bar Mamla, we did not find an answer for him until he died, and then we found an answer. [(Jerusalem Talmud, Chapter 3 of Shevuot, Halacha 4)].
In Baba Batra [(67b)], what is Mamla? Rabbi Abba bar Mamla is from the city of Melech. [(Rav bar Mamla in Baba Metzia (56b). Rav in Baba Metzia and Rav Amram (Jerusalem Talmud, Chapter 1 of Baba Metzia). Rabin in Baba Metzia (Jerusalem Talmud, Chapter 7 of the Gold), perhaps they are all one)].
Rav said [(Baba Batra 38a, and Chapter 8, 2)]. And in the Jerusalem Talmud, Chapter 1 of Makkot, Rabbi Ba in Baba Metzia, Rav Amram, Rav Matna in the name of Rav. Rabbi Abba in his name (see above). And Rabbi Abba bar Zavda, and Rabbi Abba bar Zutra.
And Rabbi Avina. And Rabbi Acha bar Yitzchak. And Rabbi Iva. They sat before Rabbi Ami (Yevamot 105a) and asked from Rabbi Ami (Baba Kamma 19a) and challenged Rabbi Ami (Baba Metzia 36a).
Rabbi Ami said to them: You told us in the name of Rabbi Yochanan Nasi (Nedarim 21a). Rabbi Ami sent to him (Baba Batra 59a). Rav Asi said to Rabbi Zeira, and afterward I asked Rabbi Abba bar Mamla (Chulin 129b). Rabbi Bon bar Chiya in his name (see above).
Rabbi Bon bar Bisna in his name, asked Rabbi Hoshaya Rabba (Jerusalem Talmud, Chapter How is the Foot). Rabbi Zevida in his name. Rabbi Zeira bar Mamla, perhaps he is his brother. Rabbi Zeira said to him (Chulin 131a) and disagreed with him (Sukkah 20b) from where (4b), Zeira before him (Shevi'it Chapter 2), and in his name (Ma'aser Sheni, Chapter 1, Halacha 2).
Rabbi Chizkiyah in his name. He challenged Rabbi Chiya bar Abba (Baba Kamma 19a, 35b, 106b) Shevuot (40b). He asked Rabbi Yehuda Nasi (Jerusalem Talmud, Chapter How is the Foot). Rabbi Yochanan in the name of Rabbi Abba bar Mamla (so too in Yichus and I did not find).
Rabbi Abba bar Mamla said: They did not hear this from Rabbi Yochanan who said, Zevachim (99b). Rabbi Yirmiyah in his name (see above). Rabbi Yitzchak Atishia taught him (see below). Rabbi Matna (see above) and Rabbi Amram (see above).
Rav said (see above). He asked before Rav (Jerusalem Talmud, Peah, Last Chapter), he asked before Rabbi Shmuel bar Yitzchak and he answered him: Rabbi Abba bar Mamla stood with Rabbi Yirmiyah and Rabbi Abba bar Mamla said to Rabbi Shmuel bar Yitzchak: See how it flies in the air what you bring as proof. Rabbi Zeira came to Rabbi Yitzchak Atishia and taught him (Jerusalem Talmud, Chapter 3 of Sotah)].
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