How can one parallelize tasks in CTR-AES for maximum performance? From what I have read it seems like one of the purported benefits of using CTR mode AES, is that it can be parallelized to a greater degree, or maybe more easily than the other block cipher modes, leading to performance gains?

In NIST SP800-38A §6.5 , it says: 


  In both CTR encryption and CTR decryption, the forward cipher functions can be performed in parallel...


And this answer to “Decryption a chunk of file with AES”, if I understand correctly, suggests that basically you have one task do $$O_j=CIPH_K(T_j) \text{ for } j=1,2...\frac{n}{2}$$ with another task doing $$O_j=CIPH_K(T_j) \text{ for } j=\frac{n}{2},\frac{n}{2}+1...n$$ in parallel. 

Is this what NIST SP800-38A, was referring to, something along these lines?
Or are there more or better ways to parallelize things?
From the diagram on CTR mode

you can notice that there are no dependencies between any of the phases of the pipeline. If you have more than one block-size worth of data, you can process each block-size chunk completely independently of the others by calculating $\mathrm{ciphertext}_i = E(\mathrm{key}, \mathrm{nonce} \, || \, \mathrm{counter}_i) \oplus \mathrm{plaintext}_i$.