Sure! Below is a Python function to generate test cases for the "Partial String Decomposition" problem.

```python
import random
import string

def generate_random_string(length):
    return ''.join(random.choices(string.ascii_lowercase, k=length))

def tcgen():
    # Generate lengths for S and T within the constraints
    len_S = random.randint(1, 2 * 10**5)
    len_T = random.randint(1, 2 * 10**5)
    
    # Generate the random strings S and T
    S = generate_random_string(len_S)
    T = generate_random_string(len_T)
    
    # Generate k such that 1 ≤ k ≤ |T|
    k = random.randint(1, len_T)
    
    return S, T, k

# Example usage
S, T, k = tcgen()
print(f"S: {S}")
print(f"T: {T}")
print(f"k: {k}")
```

Explanation of the `tcgen` function:
- `generate_random_string(length)` generates a random string of a given length composed of lowercase alphabets.
- `tcgen()` generates random lengths for `S` and `T` within the specified constraints.
- It then generates random strings `S` and `T` with those lengths.
- It picks a random integer `k` such that `1 ≤ k ≤ |T|`.
- The function returns the generated strings `S`, `T`, and the integer `k`.

This will give you varied test cases for the problem, ensuring comprehensive coverage for different scenarios within the allowed constraints.