What happens next: you don't need to have any further communication with the school. In due course, the LA will want to know what arrangements you've made for your son's education, and you'll need to tell them he's now being home educated. (If they don't happen to ask, you have no obligation to contact them and volunteer that information. There is rarely any benefit to doing so.)
The LA can and probably will ask you for some information about his home education. It's premature and pointless for them to ask about how you PLAN to home educate, as that has no legal bearing on the question of whether you ARE providing a suitable education, but most LA staff are unfamiliar with the law! So you can decline to answer any questions about the future, as those questions just waste everybody's time.
They ought to write to you, but some may phone up or even appear on your doorstep with no warning(!) and try to invite themselves to visit your home. You can simply tell them you want all correspondence in writing, and send them a report on what you're doing. You don't have to complete any forms they may send, which will almost certainly include questions which are intrusive or irrelevant, and won't ask about some of the things you might want to tell them about your child's education.
Technically you have no obligation to give the LA any information at all, but in the absence of any information, they may conclude that there is an appearance that your child isn't receiving a suitable education, and take legal action against you. It's easier to avoid that scenario by sending them something. However, it's up to you what format that information takes. They can't disregard it simply because you didn't fill in their forms or agree to let them visit or whatever they may request/demand. Some LA staff get a bit overenthused and think they can demand your compliance with whatever policies they may concoct, but they don't get to override the law.
By the way, you might prefer to post on the home ed board if you want input from people who know about home education.