The request for designing or reconstructing objects from planar cross sections arises in various applications, ranging from CAD to GIS and Medical Imaging. The present work focuses on the "one-to-many" branching problem, where one of the planes can be populated with many, possibly tortuous and densely packed, contours. The proposed method combines the proximity information offered by the Euclidean Voronoi diagram with the concept of surrounding curve and T-splines technology for securing a flexible and portable representation. Our algorithm delivers a single T-spline that deviates from the given contours less than a user-specified tolerance, measured via the so-called discrete Frechet distance and is C^2 everywhere except from a finite set of point-neighborhoods. Subject to minor enrichment, the algorithm is also capable to handle the "many-to-many" configuration as well as the global reconstruction problem involving contours on several planes.