Starting from the electric field integral equation (EFIE), it is shown how, for quasi-static cloaking (i.e. zero scattered fields), the EFIE can be reduced to classical Kirchhoff's current law (KCL). The KCL, if considered according to all-dielectric or metal-dielectric structures, is demonstrated to realise devices based on plasmonic or mantle cloaking, respectively. The KCL generalises scattering cancellation theory for arbitrary shape devices in homogeneous backgrounds and it can be extended as a local cloaking condition beyond quasi-static regime. A cloaking device can be seen as a node (i.e. no current source or sink) that ensures all current densities to be compensated even for more complicated low scattering devices.