  The top-charm associated productions via $e^+ e^-$, $e^- \gamma$ and $\gamma
\gamma$ collisions at linear colliders, which are extremely suppressed in the
Standard Model (SM), could be significantly enhanced in some extensions of the
SM. In this article we calculate the full contribution of the topcolor-assisted
technicolor (TC2) to these productions and then compare the results with the
existing predictions of the SM, the general two-Higgs-doublet model and the
Minimal Supersymmetric Model. We find that the TC2 model predicts much larger
production rates than other models and the largest-rate channel is $\gamma
\gamma \to t \bar{c}$, which exceeds 10 fb for a large part of the parameter
space. From the analysis of the observability of such productions at the future
linear colliders, we find that the predictions of the TC2 model can reach the
observable level for a large part of the parameter space while the predictions
of other models are hardly accessible.
