Certainly! Based on the problem statement for "Partial String Decomposition," here is a test case generator written in Python:

```python
import random
import string

def generate_string(length):
    return ''.join(random.choice(string.ascii_lowercase) for _ in range(length))

def tcgen():
    # Generate random lengths for S and T within the given constraints.
    len_S = random.randint(1, 2 * 10**5)
    len_T = random.randint(1, 2 * 10**5)
    
    # Generate random strings S and T of the given lengths.
    S = generate_string(len_S)
    T = generate_string(len_T)
    
    # Generate a random integer k within the constraint 1 ≤ k ≤ |T|
    k = random.randint(1, len_T)
    
    return S, T, k

# Example of generating a test case
S, T, k = tcgen()
print("S:", S)
print("T:", T)
print("k:", k)
```

This test case generator creates random strings `S` and `T` and a random integer `k` as per the constraints given in the problem statement. It ensures that:
- `S` and `T` are composed of lowercase alphabets.
- The lengths of `S` and `T` are within the range [1, 200,000].
- The integer `k` is within the range [1, len(T)].

To use this test case generator, simply run the code, and it will print out a randomly generated test case for you.