Graphene quantum dots (QDs) hold great promises in spintronics. Here, we report our predictions of honeycomb-patterned QDs beyond graphene, on the basis of first-principles calculations and an extended Hubbard model. Our calculations showed that the electronic structures and spin-polarization of boron nitride (BN) and silicon carbide (SiC) QDs can be well tuned by controlling the shape and size of the QDs. Edge hydrogenation can not only greatly improve the stability but also diminish the spin-polarization of BN-QDs. Triangular SiC-QDs have spin-polarized ground states, and the magnetic moments increase with the increase of QD size. Hexagonal SiC-QDs, however, possess spin-unpolarized ground states whose energy gaps decrease with the increase of QD size. To understand the origins of the composition- and shape-dependent spin-polarization of these honeycomb-patterned QDs, we extended the single-orbital Hubbard model of graphene QDs by taking into account the onsite energy differences of the two sublattices. Our extended Hubbard model reproduces well the results of first-principles calculations and offers a simple model to predict the electronic structures of honeycomb-patterned QDs.