'ssh' command behavior

Hi,

 I'm about to switch an application from using rsh to (Open) ssh and
bumped into a problem. My (web) application runs on Solaris and its
task is to run, control, and stop processes running on other Solaris
systems.

 If someone clicked on 'start' button, it started a local process,
which in turn started a process via rsh on the remote Solaris server.
It was like:

 rsh -l username servername '/tmp/startscript.sh'

These two processes ran until one of them died, i.e. any of these
process died, the other one died too. This way I could control exactly
whether a remote process still runs, and I also was able to stop this
exact process. In fact, rsh made the whole control of the remote
process transparent, I got the stdin, stdout, stderr of the process
locally, and even the signals sent to the local process were forwarder
exactly to the remote process.

Now, I thought I can just simply replace the rsh with ssh, I supposed
this mechanism works the same way. However, if I kill the local
process, the remote one doesn't end.

Could you please tell me, how this mechanism works on ssh?

Regards,

Zoltan