Teeth can not be usefully grown in humans at this time. There is research being done with dental stem cells to re-grow a root instead of placing a dental implant. A porcelain or zirconia crown would still be needed since that space and shape has to be custom for each situation. There does also seam to be some promise with a new drug (Tideglusib) that can stimulate dentin formation in a tooth. This could prevent the need for many root canals. The hole in the enamel will still need to be repaired since the tooth formation will be internal and not externally directed.