Abstract: We introduce a class of H-valued parabolic equations on domains, H a Hilbert space. Coupled boundary conditions of a general form are considered in dependence of a certain subspace Y of H. This construction has been introduced by Peter Kuchment: we extend it to the case of time-dependent (so-called Wentzell-Robin-type) boundary conditions. This leads to generation of an infinite family of operator semigroups governing the parabolic equation, one for each Y. Aim of this talk is to show how the choice of Y affects the properties of the associated semigroup, e.g. by characterizing its submarkovian property.