You can configure the default e-mail notifications in umbracosettings.config:

/config/umbracosettings.config

<notifications>
  <!-- the email that should be used as from mail when umbraco sends a notification -->
  <email>[email protected]</email>
</notifications>

But if you need some dynamic logic, send to specific user types or a list of fixed recipients, you will have to implement custom code subscribe the events to send the email:

https://our.umbraco.org/documentation/reference/events/contentservice-events

using Umbraco.Core;
using Umbraco.Core.Events;
using Umbraco.Core.Models;
using Umbraco.Core.Publishing;
using Umbraco.Core.Services;

namespace My.Namespace
{
    public class MyEventHandler : ApplicationEventHandler
    {

        protected override void ApplicationStarted(UmbracoApplicationBase umbracoApplication, ApplicationContext applicationContext)
        {
            ContentService.Published += ContentServicePublished;     
        }            

        private void ContentServicePublished(IPublishingStrategy sender, PublishEventArgs<IContent> args)
        {
            foreach (var node in args.PublishedEntities)
            {
                if (node.ContentType.Alias == "Comment")
                {
                    SendMail(node);
                }
            }
        }
    }
}

Note: If you need the default HTML markup, you find in the /Umbraco/Config/Lang localization file. Alias "mailBodyHtml".

Update: This blog has an interesting implementation of notification (not tested)

http://www.felinesoft.com/blog/replacing-umbraco-services-notification-service/

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