What is the latest age you see a person having growth spurts in height and can that be as late as in the mid-30s?

Sometimes at 17-19yr: In order to have a late growth spurt in height, a young person's growth plates in the leg bones must still be open (not fused closed). Usually, any late growth spurts are at age 17-19, and tend to be genetically determined, so other relatives may show a similar growth pattern. Growth spurts after age 19 are very, very unusual (and certainly won't happen in the mid-30's).