Couple interesting tidbits about AR's. They dont downregulate. Androgens are always attaching to new receptors. Standard life span ffor an AR is about 3 hrs. In the presence of excess androgens that lifespan almost doubles to around 6 hrs (ie - on cycle or even trt). Also in the presence of excess androgens the rate of production for new AR's almost doubles as well. There are limiting factors to growth and so on but androgen receptor saturation or down-regulation are not among those factors.

J Biol Chem. 1985 Jan 10;260(1):455-61.
Mechanism of androgen-receptor augmentation. Analysis of receptor synthesis and degradation by the density-shift technique.
Syms AJ, Norris JS, Panko WB, Smith RG.
The ductus deferens smooth muscle tumor cell line (DDT1MF-2) contains receptors for, and is stimulated by, androgens. Cells cultured in the absence of androgens maintain a basal level of androgen receptors. Following incubation with various concentrations of the synthetic androgen methyltrienolone (R1881) for 1-6 h, the concentration of these receptors increased from 6.0 to 12.2 fmol/micrograms of DNA, while the equilibrium dissociation constant (Kd) of 0.5 nM for this steroid remained unchanged. The steroid-induced increase in androgen receptor levels was specific for androgens and dependent upon protein synthesis. The mechanism of receptor augmentation was examined by utilization of isotopically dense amino acids to determine rates of receptor appearance and degradation in the presence or absence of [3H]R1881. In the absence of androgens, the half-life of the androgen receptor was 3.1 h, with a rate constant (kD) of 0.22/h. In the presence of 1 nM [3H]R1881, however, the half-life was 6.6 h, with kD = 0.11/h. The rate constant for receptor synthesis (ks) in the absence or presence of [3H]R1881 was calculated to be 1.35 and 2.23 fmol/micrograms of DNA/h, respectively. Thus, androgen-induced androgen-receptor augmentation is explained by an increase both in receptor half-life and in rates of receptor synthesis.