to choose (a person, group) for a job, responsibility

assign responsibility; decide

to consider something to be caused or down by a person, thing

assign to source

to give (something) for use or as a share or part

select and give a responsibility

to prove beyond doubt the origin etc of (something)

establish as real, genuine

to give (legal) power to or right of control to (a person)

give power or control

to feel sure of the truth of (something, that a person is honest etc)

trust, rely on

to declare (usually by showing a certificate) that (something is true, correct)

declare as true

to speak favourably of (a person, achievement etc)

recommend, praise

to give (a person) power or authority (to act)

authorize, enable

to make (a person) able to do something by giving authority or means

allow, authorize

to write one's name on the back of (a cheque)

support, authorize

to consider that an act, quality or result is a person's responsibility or fault

attribute

(in tennis, squash etc) a small error allowing a point to be played again; to allow (a person, thing) (to do something or to happen)

allow

to give one's formal approval to (an agreement) by signing etc

affirm, authorize

(of a speaker, what is said etc) to speak about (a person, thing); to be relevant to; to turn to, go to, (a person, thing) for information etc

mention

to put (a player, team etc) into a lower position

assign, transfer