Duties of bishopric's counselor

Is stated anywhere in the handbooks which auxiliary organizations are assigned to each counselor in the bishopric?

I don't think so. See Handbook 1: 2.1.7

Handbook 2: 10.3.1 does indicate a pairing (and implied separation) of assignments, "He assigns his counselor who works with deacons to work with the Beehives and his counselor who works with the teachers to work with the Mia Maids."

There may be others. I'd check the "Ward Leadership" section of each auxiliary in the Handbook to check for details.

luisloayza wrote:Is stated anywhere in the handbooks which auxiliary organizations are assigned to each counselor in the bishopric?

In addition to his priesthood oversight responsibilities (elders quorum, priests quorum), the bishop oversees the Relief Society. His counselors are usually assigned to oversee the other auxiliary organizations.

luisloayza wrote:Is stated anywhere in the handbooks which auxiliary organizations are assigned to each counselor in the bishopric?

No.

The bishop has assigned responsibility for Relief Society and the ward mission. Almost everything else is assigned to a counselor, but there is nothing that specifies which counselor has which assignments.

From Handbook 2:

5.1.3: Under the bishop’s direction, the ward mission leader has the following responsibilities
9.2.1: The bishop meets with the Relief Society president regularly to discuss Relief Society and welfare matters.

5 Preamble: The bishop may assign one of his counselors to coordinate convert retention and the other to coordinate activation.
8.3.1: The bishop assigns one of his counselors to oversee the ward Young Men organization under his direction.
8.3.1: The bishop assigns one of his counselors to oversee the deacons quorum and the other counselor to oversee the teachers quorum.
10.3.1: The bishop assigns one of his counselors to oversee the ward Young Women organization.
11.2.1: The bishop assigns one of his counselors to oversee the ward Primary.
12.2.1: The bishop assigns one of his counselors to oversee the ward Sunday School, including the meetinghouse library.
14.2.2: A member of the bishopric serves as the ward music adviser.

I think I got most of them.

As russellhltn pointed out, there is a correlation between Aaronic Priesthood quorums and Young Women classes, but there is not a specific assignment for which counselor has which pairing.