In this work, we propose a Boundary Informed Dynamic Graph Convolutional Network (BIDGCN) characterized by a novel boundary informed input layer, with special focus on applications related to adaptive spline approximation of scattered data. The newly introduced layer propagates given boundary information to the interior of the point cloud, in order to let the input data be suitably processed by successive graph convolutional network layers. We apply our BIDGCN model to the problem of parameterizing three-dimensional unstructured data sets over a planar domain. The parameterization problem is a key step in the solution of different geometric modeling tasks and in particular for the design of surface reconstruction schemes with smooth spline surfaces. A selection of numerical examples shows the effectiveness of the proposed approach for adaptive spline fitting with (truncated) hierarchical B-spline constructions.