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We study nodal component count of the following Gaussian Laplaceeigenfunctions: monochromatic random waves (MRW) on $\mathbb{R}^2$, arithmeticrandom waves (ARW) on $\mathbb{T}^2$ and random spherical harmonics (RSH) on$\mathbb{S}^2$. Exponential concentration for nodal component count of RSH on$\mathbb{S}^2$ and ARW on $\mathbb{T}^2$ were established by Nazarov-Sodin andRozenshein respectively. We prove exponential concentration for nodal componentcount in the following three cases: MRW on growing Euclidean balls in$\mathbb{R}^2$; RSH and ARW on geodesic balls, in $\mathbb{S}^2$ and$\mathbb{T}^2$ respectively, whose radius is slightly larger than thewavelength scale.

Concentration for nodal component count of Gaussian Laplace eigenfunctions