Two-dimensional thermal conduction between a source/sink and a body of larger size results in thermal spreading and constriction, which are of much technological importance in problems such as semiconductor thermal management. While the traditional analysis of thermal spreading and constriction assumed adiabatic side walls, there is growing interest in convective heat removal from the side walls, such as in multilayer three-dimensional integrated circuits (3D ICs) and stacked Li-ion cells in a battery pack. This work presents theoretical analysis of thermal spreading in a multilayer body with distinct convective heat transfer coefficients along the side wall for each layer, in addition to anisotropic thermal conductivity in each layer and thermal contact resistance at interfaces between layers. A series solution for the temperature distributions in each layer is derived, with a unique set of eigenvalues for each layer. A set of linear algebraic equations that govern the coefficients of the series solutions is derived. Results are shown to agree well with past work for special cases, as well as with numerical simulations for general problems. The impact of source size, thermal anisotropy and Biot numbers of various layers is analyzed in detail. In particular, the interplay between Biot numbers along the sidewall and at the sink plane in determining total thermal resistance is investigated in detail. This work contributes towards a fundamental understanding of theoretical thermal conduction in problems of practical relevance, such as advanced microelectronics and Li-ion cells. Results may find application in the design and optimization of these and other engineering systems where thermal spreading or constriction play an important role.