Maputil class shows an example on how to use Maps to form MAP<Id,List<Sobjects>>

Maputil

Map < Id, List < Contact >> mapAccIdByCntlst = new Map < Id, List < Contact >> ();

for (Contact c: [Select Id, name, AccountId from Contact where AccountId != null]) {

        // AccountId mapping with Contact List

        if (mapAccIdByCntlst.containsKey(c.AccountId)) {
                mapAccIdByCntlst.get(c.AccountId).add(c); //tricky part .Here map.get(key) is returning list and we are adding contacts to the list
        } else {
                List < Contact > lstcnts = new List < Contact > (); //Initialize list as no key is found before and first time we get key 
                lstcnts.add(c);
                mapAccIdByCntlst.put(c.AccountId, lstcnts);
        }

}