The area (A) covering a sample of non-autocorrelated animal relocations (n) is generally thought to increase asymptotically towards a true home range size with increasing sample size. This should be the case for any home range with a stable centre, whether applying a minimum convex polygon, box counting or some more sophisticated method for area demarcation. We show by simulation that the rate of increase of A is expected to decrease significantly from one m-fold increase of n to the next m-fold increase, for n as low as 100-200 relocations. For larger n the rate of increase of A is expected to be close to zero for last m-fold increase of a subsample of n. This central null hypothesis in ecology is not supported by an extensive, and assumed representative, sample of (n,A) literature data. Even after adjusting for small-n expected underestimates of A, A increases approximately in proportion with the square root of n. Literature examples are given where no area asymptote appeared in sample sizes passing thousands of relocations. The results support an alternative model for home range area use, the multiscaled home range model (MHR).