don't increase limit in doTheThing over like 5 because youtube will probs ban your IP

annotationdata.js

var urls = {
  proxy: (u) => `//crossorigin.me/${u}`,
  proxy: (u) => u,
  annotations: (id) => urls.proxy(`https://www.youtube.com/annotations_invideo?video_id=${id}`),
  isYouTube: (u) => !!u.match('https://www.youtube.com/'),
  getYouTubeID(u) {
    var res = u.match(/\?v=([^$&]+)/);
    return res ? res[1] : '';
  }
};

var parseAnnotations = function(data) {
  var doc = (new DOMParser).parseFromString(data, 'text/html').querySelector('document');
  var annotations = doc.querySelectorAll('annotation');
  return annotations;
};

var doTheThing = function(limit) {
 var data = {meta: {requests: 0, ids: []}};
 var recurse = (id, depth) => {
  data.meta.requests++;
  return fetch(urls.annotations(id))
   .then(res => res.text())
   .then(parseAnnotations)
   .then(annotations => {
    var res = [];
    annotations.forEach(a => {
     var actions = Array.from(a.querySelectorAll('action'));
     actions.forEach(act => {
      if (act.getAttribute('type') === 'openUrl') {
       var url = act.querySelector('url').getAttribute('value');
       if (urls.isYouTube(url)) {
        var id = urls.getYouTubeID(url);
        if (id) res.push(id);
       }
      }
     });
    });
    return res;
   })
   .then(ids => {
    var res = [];
    ids.forEach(aId => {
     if (aId in data) {
      data[aId].push(id);
     } else {
      data[aId] = [id];
     }
     if (depth < limit && !data.meta.ids.includes(aId)) {
      data.meta.ids.push(aId);
      res.push(recurse(aId, depth + 1));
     }
     console.log(`%c${aId}: %c${res.length}`, res.length ? 'color: blue' : 'color: #AAF', 'color: auto');
    });
    return Promise.all(res);
   });
 };

 return recurse('4gRK5f9o_yk', 0)
  .then(() => data);
};

doTheThing(2)
 .then(d => console.log('Did ' + d.meta.requests + ' requests to get', d));