During DNA replication, new nucleotides are added to the 3' end of the growing strand. This is because DNA polymerase, the enzyme responsible for replication, can only add nucleotides to the free 3'-hydroxyl group. This means that the 3' end of the DNA helix is where the new nucleotides are added, and therefore, it is the end that grows.
So, to answer your question directly: The 3' end of a DNA helix grows.