The structure of heteroepitaxial (001) lead titanate films on (001) strontium titanate and (001) magnesium oxide grown by organometallic chemical vapour deposition has been investigated. PbTiO3 grows textured on (001)MgO and heteroepitaxially on (001)SrTiO3. Details of the microstructure are, however, comparable. Rutherford backscattering spectrometry (RBS) channelling experiments on heteroepitaxial PbTiO3 films on (001)SrTiO3 have shown that the microstructure is dominated by the layer thickness. The cooling rate is found to have no influence on the microstructure. Very thin films to about 50 nm thickness show a relatively large value of the minimum channelling yield which decreases with increasing thickness. For film thicknesses between about 50 nm and 100 nm the minimum channelling yield is relatively low, down to a few percent, indicative of high-quality epitaxial films. If the him thickness exceeds a critical value of about 100 nm the epitaxial quality deteriorates as can be concluded from the sharp increase in the value for the minimum yield. Changes in minimum yield are due to changes in the microstructure of the film which has been studied by transmission electron microscopy (TEM) and X-ray diffraction. TEM and {100}PbTiO3 pole-figure measurements show the presence of a-axis oriented domains sharing {101} twin planes with the c-axis matrix. The volume fraction has been estimated from theta-2 theta scans as a function of offset in theta. For thick films the volume fraction scales with the minimum yield. This analysis is confirmed by rocking-width measurements. The presence of non-uniform residual strain in the film has been analyzed from broadening of the (001)PbTiO3 diffraction lines. Details of the microstructure are correlated with the RES data. A tentative interpretation is presented.