The query to list the tables and their records count in a specific database.

SELECT
QUOTENAME(SCHEMA_NAME(sOBJ.schema_id)) + '.' + QUOTENAME(sOBJ.name) AS [TableName]
, SUM(sPTN.Rows) AS [RowCount]
FROM
sys.objects AS sOBJ
INNER JOIN sys.partitions AS sPTN
ON sOBJ.object_id = sPTN.object_id
WHERE
sOBJ.type = 'U'
AND sOBJ.is_ms_shipped = 0x0
AND index_id < 2 -- 0:Heap, 1:Clustered
GROUP BY
sOBJ.schema_id
, sOBJ.name
ORDER BY [TableName]
GO