A method and kit for the capture and purification of specific nucleic acids from a sample with affinity capture probes on a solid support and for the replication of said nucleic acids with a strand displacing polymerase, whereby a second primer complementary to a sequence in each of the target nucleic acids distinct from that bound by capture probes is also bound to the nucleic acid targets, and extension of one of the primers on each target effects the separation of the copied nucleic acid strands from the solid support. Incorporation of universal nucleic acid sequences during their replication enables the simultaneous and highly specific amplification of multiple nucleic acid target sequences with minimal production of artifacts.