Tom Cruise and Katie Holmes
07/11/2008 AT 06:30 AM EDT
The Cruise family has sent along a present to welcome little Sunday Rose Kidman Urban
, PEOPLE has learned.
Contrary to some reports that Tom Cruise
gave ex-wife Nicole Kidman
a "room full of flowers," the actor and his family – including Cruise's children with Kidman, Bella, 15, and Connor, 13 – actually sent a huge baby basket to Nashville.
The high-end gift included chenille Giraffe baby blankets, items from the Hermes baby line and other newborn necessities.
Kidman, 41, gave birth
to Sunday Rose at a Nashville hospital on Monday morning, with husband Keith Urban
, 40, by her side for the smooth delivery.
"We feel immensely blessed and grateful to be given this beautiful baby girl," the happy couple said in an exclusive statement to PEOPLE. "She's an absolute delight."