A tree cover of a graph G is defined as a collection of trees such that their union includes all the vertices of G. The cost of a tree cover is the weight of the maximum weight tree in the tree cover. Given a positive integer k, the k-tree cover problem is to compute a minimum cost tree cover which has no more than k trees. Star covers are defined analogously. Additionally, we may also be provided with a set of k vertices which are to serve as roots of the trees or stars. In this paper, we provide constant factor approximation algorithms for finding tree and star covers of graphs, in the rooted and un-rooted versions.