A method of fabricating composite substrates by associating a transfer layer with an intermediate support to form an intermediate substrate of predetermined thickness with the transfer layer having a free surface; providing a sample carrier having a surface and a recess that has a depth that is approximate the same as the predetermined thickness of the intermediate substrate so that the transfer layer free surface is positioned flush with the sample carrier surface; providing a support layer both on the transfer layer free surface and on a portion of the sample carrier surface surrounding the recess; removing the portion of the support layer that extends beyond the intermediate substrate; and detaching the transfer layer and support layer from its intermediate support to form the composite substrate. The support layer is made of a deposited material that has a lower quality than that of the intermediate support. A bonding layer may be included on one of the intermediate support or the useful layer, or both, to facilitate bonding of the layers. The final substrates are useful in optic, electronic, or optoelectronic applications.