how to merge dimensional arrays

If I understand you correctly, you want it compact by id.

function getCompactById(arr) { // must have the same id    var res = [];    var obj = {};    obj.id = arr[0][0].id;    obj.children = [];    for(var i = 0; i < arr.length; i += 1) {        obj.children.push(arr[i][0].children[0]);    }    res.push(obj);    return res;}

The array looks like var arr = [list1, list2]; In the function create an array and an object. The object gets an id and an array. The id is always the same, so we take it from the first array. Go through the array and push all objects arr[i][0].children[0]. After the loop push the obj in the array. Return the result array.

Demo

The following code will merge all levels of the two tree arrays, not just on the upper most level:

var list1 = ...var list2 = ...var addNode = function(nodeId, array) {  array.push({id: nodeId, children: []});};var placeNodeInTree = function(nodeId, parent, treeList) {  return treeList.some(function(currentNode){    // If currentNode has the same id as the node we want to insert, good! Required for root nodes.    if(currentNode.id === nodeId) {      return true;      }    // Is currentNode the parent of the node we want to insert?    if(currentNode.id === parent) {      // If the element does not exist as child of currentNode, create it      if(!currentNode.children.some(function(currentChild) {        return currentChild.id === nodeId;      })) addNode(nodeId, currentNode.children);      return true;    } else {      // Continue looking further down the tree      return placeNodeInTree(nodeId, parent, currentNode.children);    }  });};var mergeInto = function(tree, mergeTarget, parentId) {  parentId = parentId || undefined;  tree.forEach(function(node) {    // If parent has not been found, placeNodeInTree() returns false --> insert as root element    if(!placeNodeInTree(node.id, parentId, mergeTarget)){      list1.push({id: node.id, children:[]});    }    mergeInto(node.children, mergeTarget, node.id);  });};mergeInto(list2, list1);document.write('<pre>');document.write(JSON.stringify(list1, null, 4));document.write('</pre>');

See the code live on JSBin: http://jsbin.com/wikaricita/3/edit?js,output

Note that it this algorithm has a complexity of O(n^2), which means that it will not scale really well. If the trees get very big or performance is a critical issue, you probably want to look into other ways of solving this problem.