  We investigate K\"ahler metrics conformal to gradient Ricci solitons, and
base metrics of warped product gradient Ricci solitons. The latter we name
quasi-solitons. A main assumption that is employed is functional dependence of
the soliton potential, with the conformal factor in the first case, and with
the warping function in the second. The main result in the first case is a
partial classification in dimension $n\geq 4$. In the second case, K\"ahler
quasi-soliton metrics satisfying the above main assumption are shown to be,
under an additional genericity hypothesis, necessarily Riemannian products.
Another theorem concerns quasi-soliton metrics satisfying the above main
assumption, which are also conformally K\"ahler. With some additional
assumptions it is shown that such metrics are necessarily base metrics of
Einstein warped products, that is, quasi-Einstein.
