<p>We investigate a quantum controlled teleportation via an arbitrary entangled three-qubit pure state in the most general form. We investigate it by analysing one-qubit teleportation via an arbitrary four-term entangled two-qubit state and applying the result to the controlled teleportation. In this work, the controller uses the computational or Hadamard basis as the measurement basis. As a result, we show relationships between the channel state coefficients that can be used as criteria to determine whether a controlled teleportation protocol becomes deterministic, i.e., has unit probability and fidelity; probabilistic, i.e., has unit fidelity but less than one probability; or no teleportation occurs, i.e., with unit fidelity. Uniquely, the evaluation is done by examining the channel state’s coefficients alone. In particular, if the controller uses the computational basis, it is impossible to perform deterministic quantum controlled teleportation using only two, three, five, six, or seven non-zero-term channel states. Lastly, we briefly discuss the impact of noise, where a more diverse state may be required to achieve better performance. The results in this paper can be used as guidance to choose which quantum state performs best when used in teleportation under certain types of noise.</p>