Possible Clues:

• Cutting vessel, jugular vein's fluid all over the place
• Bath, say, girl left clutching small blanket
• Remarkably alive, runs all round
• Film studio and theme park, marketed as the “Entertainment Capital of LA”
• Runs a live broadcast, worldwide
• Catholic sort of joint
• Valise, urn, box - applicable to all cases?
• Global virus heartless alien spread
• Vain rules, unexpectedly widespread
• Blanket unravels badly, one's admitted