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We discuss the joint temporal and contemporaneous aggregation of N independent copies of random-coefficient AR(1) processes driven by independent and identically distributed innovations in the domain of normal attraction of an
$0< \alpha \le 2$
, as both N and the time scale n tend to infinity, possibly at different rates. Assuming that the tail distribution function of the random autoregressive coefficient regularly varies at the unit root with exponent
$\beta > 0$
, we show that, for
$\beta < \max (\alpha, 1)$
, the joint aggregate displays a variety of stable and non-stable limit behaviors with stability index depending on
and the mutual increase rate of N and n. The paper extends the results of Pilipauskaitė and Surgailis (2014) from
$0 < \alpha < 2$
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