We present results from a numerical investigation of the coiling patterns obtained when a slender elastic rod is deployed onto a moving substrate. The Discrete Elastic Rods method is employed to explore the parameter space, construct phase diagrams, identify their phase boundaries and characterize the pattern morphology. The various length scales of the patterns are primarily set by the gravity-bending length and depend only logarithmically on the deployment height. The curvature near the contact point, together with the dimensionless speed mismatch between deployment and the belt, dictate the characteristics of the patterns. The phase boundaries are found to be independent of both the gravito-bending length and the deployment height, as long as the latter is above a threshold value. We also evaluate the relative importance of twist and curvature strains, which confirms that bending has a dominant role.