About Khamma ben Nachum II, 5th Exilarch Huna I
Huna Kamma (Aramaic/Hebrew: הונא קמא, lit. Huna I); was a Jewish Tanna sage of the fifth generation of the Tannaim era. He was an Exilarch, head of the Jewish exile in Babylon, during the days of Judah haNasi who contemporaneously was active in the Land of Israel, during the fifth generation of the Tannaim. He is a descendant of the House of David, and was recorded on the Talmud merely as R. Huna, which caused confusion between him and the Amora sage of the second generation, that was recorded on the Talmud with the same name, and was known to be a disciple of Abba Arika, and thus R. Sherira Gaon referred to him, on his epistle (Iggeret Rav Sherira Gaon), as Huna Kamma  (Kamma in Aramaic = the first), in order to distinguish him form the Amora sage of the second generation, and thereafter, the Achronim and Geonim sages began referring to him in the same appellation as well.
Judah haNasi who contemporaneously was active in the Land of Israel, and was president ("Nasi") of the Sanhedrin, located at the time in the Galilee, a position that was considered at the time the most ranked one in the Land of Israel, had asked R. Hiyya, concerning his obligation to "Korban Nasi" (leader's sacrifice) over sins he might have, a question that basically meant whether he had the status of a king or not (and on the non-practical level, since the Temple in Jerusalem was at the time in ruins to be sacrificing any). R. Hiyya replied: "You have your rival in Babylon".
—B. Talmud, Tractate Horayoth, 11b
During the Hadrianic persecution several scholars of standing, R. Yochanan Ha-Sandlar, R. Eleazar b. Shamua and other pupils of R. Akiva settled temporarily in Babylonia and thus enhanced its prestige. However, the masterful personality of the patriarch R. Judah I still dominated from Israel. There were at least five Babylonians at his court, and he claimed and was accorded the right to ordain judges for Babylonia also. R. Judah HaNasi did indeed admit the genealogical superiority of the exilarch, R. Huna, but only at a safe distance.
Rival or as in Hebrew צרה, which lit. means trouble, is a biblical phrase used to describe the "other woman"; hence, the most ranked position is held by two people, accordingly "Nasi" and "Exilarch" are equal in their status, and consequently, you are not the sole leader, which would have meant you are obliged to sacrifice a king's offering, or enjoy such a status.
1 Iggeret Rav Sherira Gaon, Da'at Encyclopedia; Full text (Hebrew) 2 i.e. the biblical story on Sarah and Hagar; "your trouble" = your husband's other woman