We present results of first-principles calculations on the transport properties, both under an electric field or a temperature gradient, in the Co/Cu multilayered systems. The various effects brought about by the changes in the morphological parameters, such as the number of repeats and the layer thickness, are discussed in a systematic way. Our calculations show that the Seebeck coefficient and the magnetothermopower (MTP) converge rather rapidly with the number of Co repeats. In the range of thin Co layers, we find strong variations in the amplitude and sign of both the Seebeck coefficient and the MTP. These large variations, which have no correspondent in the (magneto)conductance, are shown to be the result of quantum well states present in the minority spin channel of thin Co layers.