An infinite partial word is said to be *uniformly recurrent * if every factor of length *R*(*n*) contains every subword of length *n*.
The function *R*(*n*) is called the *recurrence function* of the infinite word.
Here we study those words whose recurrence functions do not grow too quickly (e.g. sublinearly).

*Keywords*: Combinatorics on words; Partial words; Subword complexity; Recurrent words