Sure! Here is the test case generator for the "Mysterious Dungeons" problem:

```python
import random
import string

def generate_dungeon(W, H):
    dungeon = [['#' for _ in range(W)] for _ in range(H)]
    
    # Place '@' and '<'
    start_x, start_y = random.randint(1, H-2), random.randint(1, W-2)
    while True:
        exit_x, exit_y = random.randint(1, H-2), random.randint(1, W-2)
        if (exit_x, exit_y) != (start_x, start_y):
            break
    dungeon[start_x][start_y] = '@'
    dungeon[exit_x][exit_y] = '<'
    
    # Place rocks and carpets
    num_labels = random.randint(1, 8)
    labels = random.sample(string.ascii_lowercase, num_labels)
    for label in labels:
        carpet_x, carpet_y = random.randint(1, H-2), random.randint(1, W-2)
        while dungeon[carpet_x][carpet_y] != '.':
            carpet_x, carpet_y = random.randint(1, H-2), random.randint(1, W-2)
        dungeon[carpet_x][carpet_y] = label
        
        rock_x, rock_y = random.randint(1, H-2), random.randint(1, W-2)
        while dungeon[rock_x][rock_y] != '.':
            rock_x, rock_y = random.randint(1, H-2), random.randint(1, W-2)
        dungeon[rock_x][rock_y] = label.upper()
    
    # Fill remaining cells with empty spaces '.'
    for i in range(1, H-1):
        for j in range(1, W-1):
            if dungeon[i][j] == '#':
                dungeon[i][j] = '.'
    
    return dungeon

def tcgen():
    test_cases = []
    while True:
        W = random.randint(3, 30)
        H = random.randint(3, 30)
        dungeon = generate_dungeon(W, H)
        
        test_case = [f"{W} {H}"]
        test_case.extend([''.join(row) for row in dungeon])
        test_cases.append('\n'.join(test_case))
        
        if random.random() < 0.1:  # Randomly decide to stop generating more test cases
            break
    
    # Add terminating line "0 0"
    test_cases.append("0 0")
    
    return '\n'.join(test_cases)

# Example usage
print(tcgen())
```

### Explanation:

1. **generate_dungeon(W, H)**:
   - This function generates a dungeon grid of size `W x H`.
   - It places the start position `@` and the exit `<` ensuring they are not in the same cell.
   - It randomly places carpets (lowercase letters) and corresponding rocks (uppercase letters).
   - The remaining cells are filled with empty spaces `.`.

2. **tcgen()**:
   - This function generates multiple test cases until a random stopping condition is met.
   - Each test case is generated by calling `generate_dungeon(W, H)` with random dimensions.
   - The test cases are formatted as specified in the problem statement.
   - Finally, it appends the line `"0 0"` to indicate the end of input.

This generator ensures a variety of test cases, including different dungeon sizes and configurations of carpets and rocks.