How or from whom does a child get plantar warts?

Same goes. The same infective process holds for children as adults. Children have have an increased ability to catch the virus because of increased exposure and activity levels.
Warts are a virus. Warts are caused by a virus and can be picked up from any surface if there is an opening in the foot.

Related Questions

Is it true that if you've had one strain of hpv, you can't get any others? I had 2 plantar warts when I was a child and one wart on hand 2 years ago.

No. Each strain has its own characteristics and immunity gained by an infection to one does not protect you from the others. The present best protection against the std forms of hpv is a vaccine with 4 separate strains covered by material in the shot.Even then, the >50 other strains of this family of viruses are unaffected. Read more...