New terminator window on remote server

The answer to this problem for terminator and remote systems is to create a terminator profile, where the command it runs 'as a login shell' is the SSH connection string used to access the remote server. It is prefered to have SSH key based authentication or openssh controlmaster/controlpath setup to have connection sharing.

Exerpt of a terminator config for this:

~/.config/terminator/config

[profiles]
[[default]]
 scroll_on_output = False
 exit_action = restart
 scrollback_infinite = True
[[remotehost]]
 use_custom_command = True
 exit_action = restart
 custom_command = ssh user@remotehost

And simply run terminator -p remotehost to use this profile. Each time you 'split' terminals, it uses this profile and thus opens a new SSH connection.

For ssh controlmaster, see: http://www.debian-administration.org/articles/290

ClonedSplittingMenu Terminator plugin (https://github.com/ilgarm/terminator_plugins) is what you are looking for. It adds Clone horizontally, Clone vertically menu items and allows reopening of ssh session by splitting the window. Installation is straightforward

mkdir -p ~/.config/terminator/plugins
cd ~/.config/terminator/plugins
wget --no-check-certificate https://github.com/ilgarm/terminator_plugins/raw/master/clone_session.py
# Restart Terminator, go to plugin menu and activate ClonedSplittingMenu plugin

Also checkout a blog post about the plugin http://lazylabs.org/blog/terminator-plugin-to-clone-current-ssh-session/