**Solution:**

Given:
- An alloy AB of 30g contains 30% A.
- The molten AB on cooling curve gave out B and a eutectic alloy with A and B at equal percentage.

**Step 1: Calculate the weight of A and B in the initial alloy AB.**

The weight of A in the alloy AB can be calculated using the percentage composition formula:

Weight of A = (Percentage of A / 100) * Total weight of AB
= (30 / 100) * 30g
= 9g

Since the alloy AB contains 30% A, the weight of B can be calculated as the difference between the total weight of AB and the weight of A:

Weight of B = Total weight of AB - Weight of A
= 30g - 9g
= 21g

Therefore, the initial alloy AB contains 9g of A and 21g of B.

**Step 2: Determine the weight of the eutectic alloy formed.**

According to the given information, the eutectic alloy is formed with A and B at equal percentages. This means that the weight of A and B in the eutectic alloy will be the same.

Let the weight of the eutectic alloy be x grams.

Weight of A in the eutectic alloy = Weight of B in the eutectic alloy = x

Since the weight of A and B in the eutectic alloy are equal, we can write the following equation:

Weight of A + Weight of B = x + x
= 2x

Since the eutectic alloy is formed by the cooling of the molten AB, the total weight of A and B in the eutectic alloy should be the same as the weight of A and B in the initial alloy AB.

Therefore, we can write the following equation:

Weight of A + Weight of B = Weight of A in AB + Weight of B in AB
= 9g + 21g
= 30g

Substituting the value of 2x from the first equation into the second equation, we get:

2x = 30g

Solving for x, we get:

x = 15g

Therefore, the weight of the eutectic alloy formed is 15g.

**Step 3: Determine the weight of B that has formed.**

Since the weight of B in the eutectic alloy is equal to x, the weight of B that has formed can be calculated as:

Weight of B that has formed = Weight of B in the eutectic alloy - Weight of B in the initial alloy AB
= 15g - 21g
= -6g

The negative value indicates that B has not formed in sufficient quantity in the eutectic alloy. Therefore, no B has formed.

In conclusion, based on the given information, no B has formed during the cooling of the molten AB.