Overstaying a visa after the 60 day grace period equals becoming illegal. That is why Miami is the way it is, people came on visas and overstayed thus became illegal by doing so. We read stories here in South Florida all the time that these people who overstayed a visa are being deported 10 or more years later. If a relative does sponsor you then you have to wait to get a work permit which you apply for when you apply for a greencard. If you overstayed and worked after your visa expires you are breaking the law. If an immediate relative who is a citizen sponsors you and a child is under 21 then it doesn't take long to get a visa or temporary greencard and a work permit. If the sponsor is a resident you have to wait up to 7 years and cannot even get a work permit during the time you are waiting. It is quicker for a relative to get citizenship under normal circumstances and then file for relatives. I know about this as I was an immigrant myself and have relatives going through the process at this time.