A realized covariance model specifies a dynamic process for a conditional covariance matrix of daily asset returns as a function of past realized variances and covariances. We propose parsimonious parameterizations enabling a spillover effect in the conditional variance equations, and a specific nonlinear, time-varying, impact of the lagged realized covariance between each asset pair on the corresponding conditional covariance. We introduce these parameterizations in BEKK, DCC and HAR type scalar models. In an application relative to the components of the Dow Jones index, we find that the extended models improve the fit and the out-of-sample forecast performances of their less flexible scalar versions.