Pipelines and function execution

Although pipelines are written sequentially with each element following the previous one, function execution in a pipeline is somewhat different. In order to illustrate this, consider the following advanced functions that all allow pipeline input:

function A{
[CmdletBinding()]
Param([Parameter(ValueFromPipeline=$true)]$x)
  begin { Write-Host "A in begin"}
  process { Write-Host "A in Process{}"
           Write-Output $x }
  end { Write-Host "A in end"}
}
function B{
[CmdletBinding()]
Param([Parameter(ValueFromPipeline=$true)]$y)
  begin { Write-Host "B in begin"}
  process { Write-Host "B in Process{}"
           Write-Output $y }
  end { Write-Host "B in end"}
}
function C{
[CmdletBinding()]
Param([Parameter(ValueFromPipeline=$true)]$z)
  begin { Write-Host "C in begin"}
  process { Write-Host "C in Process{}"
           Write-Output $z }
  end { Write-Host "C in end"}
}

The only thing these functions do is display a message when one of the three Begin-Process...