When you type Start /?, you receive:

Starts a separate window to run a specified program or command.                              START \["title"\] \[/Dpath\] \[/I\] \[/MIN\] \[/MAX\] \[/SEPARATE | /SHARED\]                                    \[/LOW | /NORMAL | /HIGH | /REALTIME | /ABOVENORMAL | /BELOWNORMAL\]                                    \[/WAIT\] \[/B\] \[command/program\]                                    \[parameters\]                                  "title"     Title to display in  window title bar.                                  path        Starting directory                                  B           Start application without creating a new window. The                                              application has ^C handling ignored. Unless the application                                              enables ^C processing, ^Break is the only way to interrupt                                              the application                                  I           The new environment will be the original environment passed                                              to the cmd.exe and not the current environment.                                  MIN         Start window minimized                                  MAX         Start window maximized                                  SEPARATE    Start 16-bit Windows program in separate memory space                                  SHARED      Start 16-bit Windows program in shared memory space                                  LOW         Start application in the IDLE priority class                                  NORMAL      Start application in the NORMAL priority class                                  HIGH        Start application in the HIGH priority class                                  REALTIME    Start application in the REALTIME priority class                                  ABOVENORMAL Start application in the ABOVENORMAL priority class                                  BELOWNORMAL Start application in the BELOWNORMAL priority class                                  WAIT        Start application and wait for it to terminate                                  command/program                                              If it is an internal cmd command or a batch file then                                              the command processor is run with the /K switch to cmd.exe.                                              This means that the window will remain after the command                                              has been run.                                              If it is not an internal cmd command or batch file then                                              it is a program and will run as either a windowed application                                              or a console application.                                  parameters  These are the parameters passed to the command/program
Using this syntax, you should be able to type start "My Windows Title" "%USERPROFILE%\My Documents\test.bat" "P 1" "p 2" "p 3"

When you do, you receive a My Windows Title command windows with the following error:

'C:\Documents' is not recognized as an internal or external command, operable program or batch file.

NOTE: when you use start "%USERPROFILE%\My Documents\test.bat" "P 1" "p 2" "p 3", you receive:

The system cannot find the file P 1.

When you run call "%USERPROFILE%\My Documents\test.bat" "P 1" "p 2" "p 3"
or just "%USERPROFILE%\My Documents\test.bat" "P 1" "p 2" "p 3", the command runs as expected.

To workaround this behavior, you can use the Start command by specifying the /D switch:

start "My Windows Title" /D"C:\%USERPROFILE%\My Documents" test.bat "P 1" "p 2" "p 3"