good, great, wide
rapid
gradual, slow
geographical, global
The current survey will have a wider geographical spread.

encourage, promote
Such unhygienic conditions encourage the spread of disease.

halt, prevent, stem, stop, tackle
combat, contain, control, curb, limit, reduce, slow (esp. AmE)

spread of
the spread of fire

centre/center
A photograph of the star adorned the centre/center spread.

double, double-page (esp. BrE), two-page
five-page, 20-page, etc.
full-page
fashion, photo

be featured in a spread, feature in a spread
She is featured in spreads in Vogue.
Her work featured in a two-page spread in ‘New Woman’ magazine.

carefully
out
We spread the rug out on the floor.

across, on, over

spread sth open
He had a newspaper spread open on his knee.

spread your arms, legs, etc. out wide, spread your arms, legs, etc. wide
a bird with its wings spread wide

fast, like wildfire, quickly, rapidly, soon
The news spread like wildfire.

gradually, slowly
easily
The disease spreads easily.

widely
Allow plenty of space for this plant as its roots spread widely.

far and wide
His fame had spread far and wide.

outwards/outward

(all) across, among, around, beyond, by, from, into, (all) over, through, throughout, to
The effects of this policy spread far beyond children now at school.
The disease can be spread by contact.
The fire rapidly spread to adjoining buildings.

be thinly spread
Expertise in this field is very thinly spread across the country.

spread yourself too thin
With four markets to manage, there's a danger that's she's spreading herself too thin.

thickly
lightly, thinly
evenly
Don't make the paste too thick, or it will not spread evenly.

on
He spread marmalade on the toast.

with
Spread each slice generously with butter.

equally, evenly, uniformly
unevenly

try to

among, between
We tried to spread the workload evenly between the departments.

over
The course takes forty hours, spread over twenty weeks.

Spread is used with these nouns as the subject:
awareness, blaze, blood, blush, butter, cancer, crack, discontent, disease, effect, epidemic, fame, fire, flame, flush, infection, mosquito, news, panic, plague, rash, religion, revolt, revolution, ripple, rumour, sensation, silence, smile, stain, story, strike, violence, virus, war, warmth, weed, word

Spread is used with these nouns as the object:
ash, bread, butter, chocolate, cost, democracy, disease, faith, fertilizer, finger, frosting, germ, gospel, gossip, hand, HIV, honey, icing, ideology, infection, influence, investment, jam, jelly, joy, knowledge, leg, load, manure, margarine, message, misinformation, mixture, mustard, myth, net, news, palm, panic, plague, poison, pollen, propaganda, religion, repayment, risk, rumour, seed, story, teaching, terror, toast, virus, wealth, wing, word, workload, wreckage