The random topology model approximately predicts all orientation-free empirical laws of channel network planform. Explanation of the model's success has crucial significance for research direction. Shreve <1975> proposed the explanation that random factors dominate network development. An alternative explanation is that these geomorphologic laws are insensitive to topologic variability. Kirchner <1993> tested the sensitivity of the Horton ratios to particular types of topologic distribution. We extend the work of Kirchner to all orientation-free empirical laws of channel network planform. We test the sensitivity of the topologic analog of each law using non-topologically random network test samples. One type of sample is obtained with the stochastic variable-parameter Q model of network growth, used as a test example, where the probability of tributary development on interior and exterior links is allowed to vary. We show that the coefficients of all channel network and planform laws vary with model parameter Q. It is possible that these laws are sensitive also to other models of network growth. We conclude that the success of the random model in approximately predicting geomorphologic laws may not be due to the insensitivity of these laws and is a result that remains unexplained.¿ 1997 American Geophysical Union