General synonyms:
* Allocate: To assign or set aside for a particular purpose.
* Disburse: To pay out money.
* Disseminate: To spread or circulate widely.
* Dispatch: To send or convey something to a destination.
* Deliver: To bring something to a person or place.
* Hand out: To give something to each person in a group.
* Spread: To extend over a wider area.
* Share: To give a part of something to someone else.
More specific synonyms:
* Apportion: To divide something into shares.
* Dispense: To give out something in portions.
* Disseminate: To spread information or knowledge widely.
* Circulate: To move something around a group.
* Scatter: To spread something randomly.
* Deploy: To move something into position for use.
Formal synonyms:
* Disseminate: To spread information or knowledge widely.
* Diffuse: To spread something gradually.
* Proliferate: To increase rapidly in number.
The best synonym for "distribute" will depend on the specific context and the meaning you want to convey.