Let K⊂Cbe compact and triangular schemes of nodes inKand poles inC\K be specified. We obtain necessary and sufficient conditions on the distribution of the poles and nodes such that every functionfholomorphic onKmay be approximated uniformly onKby a sequence of rational functions with the given poles which interpolate ∫ in the given nodes. We then show that certain point systems known to be well suited in other interpolation problems may be used successfully in our case. Suppose G⊂Cis a multiply connected domain. We then show that those point systems may be employed similarly to define sets of poles inC\G and sets of nodes inGsuch that every function ∫ holomorphic inGis the limit of the associated rational interpolants locally uniformly inG.