how does claiming HOH effect the dependants tax status?

My son has been living with me for several years now. He was married a few years back and now has a 2 year old son. They all live with me (rent free, and do not share in any of the upkeep of home) I have never claimed HOH while he has lived with me. My question is how does and will me claiming HOH effect his taxes? (how should he file his taxes?)  He is self employed. I don't want to effect his taxes. If in fact I decide to claim HOH, how far can I go back and amend my taxes? and if I amend does that mean my son has to go back and amend also?