There is no particular 'proper' way to see all the tables. Obviously, though, if you click on a table and choose Table Tools|Table Tayout>Select>Table, you can see where the boundary between two adjoining tables is.

The simplest way to avoid the splitting you're seeing is to make sure the source & destination tables have the same Table Style. If you need to append rows from a table having a different Table Style, you can change the Table Style of the pasted table after it's been pasted. It will then merge with the destination table.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]