  This paper describes the structure of the nodal set of segregation profiles
arising in the singular limit of planar, stationary, reaction-diffusion systems
with strongly competitive interactions of Lotka-Volterra type, when the matrix
of the inter-specific competition coefficients is asymmetric and the
competition parameter tends to infinity. Unlike the symmetric case, when it is
known that the nodal set consists in a locally finite collection of curves
meeting with equal angles at a locally finite number of singular points, the
asymmetric case shows the emergence of spiraling nodal curves, still meeting at
locally isolated points with finite vanishing order.
