Answer:

mushroom

Answer	Crossword Clue
MUSHROOM	Grow exponentially
MUSHROOM	Grow out of control
MUSHROOM	Fairy ring component

MUSHROOM	Grow quickly
MUSHROOM	Pizza topping
MUSHROOM	Grow rapidly.
MUSHROOM	Whereon Alice found the Caterpillar.
MUSHROOM	Where Alice met the Caterpillar.
MUSHROOM	Grow fast.
MUSHROOM	Sauce ingredient
MUSHROOM	Place to bill and coo?

MUSHROOM	Veggie
MUSHROOM	Grow and spread quickly
MUSHROOM	Cream soup
MUSHROOM	Grow unchecked