I guess this is what you need:

getTree = (path, nodes = []) => {
  // Split by levels
  const parts = path.split('/')
  // Remove last node from path and add to nodes array
  nodes.push({ name: parts.pop(), path })
  // Update path without last node (already added)
  path = parts.join('/')
  if (path.length) {
    // Recall method recursively if nodes left
    return getTree(path, nodes)
  } else {
    // Or add root node to array and return it
    nodes.push({ name: '/', path: '/' })
    return nodes
  }
}

Usage:

const path = '/root/user/home/ubuntu'
console.log(getTree(path))

Output:

[
  {name: 'ubuntu', path: '/root/user/home/ubuntu'}
  {name: 'home', path: '/root/user/home'}
  {name: 'user', path: '/root/user'}
  {name: 'root', path: '/root'}
  {name: '/', path: '/'}
]

If i understood your question correctly, you could do something like this

By using Array.prototype.split() to split the path into parts, and setting the first argument (the base) as the home and the rest of the arguments as the resultant path

const string = 'home/ubuntu/test';
console.log(parse(string));
console.log(parse('home/'));
console.log(parse('/'));

function parse(str) {
    const obj = {};
    const strArr = str.split('/');

    obj['home'] = strArr[0] ? strArr[0] : '/';
    const path = strArr.slice(1, strArr.length).join('/');

    obj['path'] = path ? path : '/';
    return obj;
}

P.S if this is not what you meant please let me know in the comments