The problem here Max is that it tests column A to find the last row, and so
misses those tail blanks.

Best to use a more generic lastrow function

Option Explicit

Public Sub ProcessData()
Const TEST_COLUMN As String = "A"    '<=== change to suit
Dim i As Long
Dim iLastRow As Long
Dim iRow As Long
Dim sh As Worksheet
Dim shName As String

   With ActiveSheet

       iLastRow = LastRow(ActiveSheet)
       For i = 2 To iLastRow
           If IsError(.Cells(i, TEST_COLUMN).Value) Then
               shName = "Err"
           ElseIf .Cells(i, TEST_COLUMN).Value = "" Then
               If .Cells(i, TEST_COLUMN).HasFormula Then
                   shName = "NS"
               Else
                   shName = "Blanks"
               End If
           Else
               shName = .Cells(i, TEST_COLUMN).Value
           End If
           Set sh = Nothing
           On Error Resume Next
               Set sh = Worksheets(shName)
           On Error GoTo 0
           If sh Is Nothing Then
               Set sh = Worksheets.Add
               sh.Name = shName
               .Rows(1).Copy sh.Range("A1")
               iRow = 2
           Else
               iRow = sh.UsedRange.Rows.Count + 1
           End If
           .Rows(i).Copy sh.Range("A" & iRow)
       Next i
       .Activate
   End With

End Sub

Function LastRow(sh As Worksheet)
   On Error Resume Next
   LastRow = sh.Cells.Find(What:="*", _
                           After:=sh.Range("A1"), _
                           Lookat:=xlPart, _
                           LookIn:=xlFormulas, _
                           SearchOrder:=xlByRows, _
                           SearchDirection:=xlPrevious, _
                           MatchCase:=False).Row
   On Error GoTo 0
End Function