In epitaxial heterostructures Pb0.5Sr0.5TiO3/La0.5Sr0.5CoO3/MgO(001) with a large lattice mismatch, ferroelectric domains and properties were experimentally studied. In 130 nm thick polydomain tetragonal Pb0.5Sr0.5TiO3 films, random arrays of similar to 0.1-0.5 mu m sized a- and c-domains are found. In vertical capacitors with Pt top electrodes, a steplike switching of polarization is observed. The results are discussed in terms of island growth and different switching mechanisms in a-and c-domains. (C) 2010 American Institute of Physics. [doi:10.1063/1.3519977]